메뉴 건너뛰기




Volumn 9781421408583, Issue , 2012, Pages 1-305

Least squares data fitting with applications

Author keywords

[No Author keywords available]

Indexed keywords


EID: 84917506005     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Book
Times cited : (152)

References (265)
  • 1
    • 85088185199 scopus 로고    scopus 로고
    • Advanced algorithms for design and optimization of quiet supersonic platforms
    • AIAA Paper 02-0114, Reno, NV
    • J. J. Alonso, I. M. Kroo and A. Jameson, "Advanced algorithms for design and optimization of quiet supersonic platforms." AIAA Paper 02-0114, 40th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, 2002.
    • (2002) 40th AIAA Aerospace Sciences Meeting and Exhibit
    • Alonso, J.J.1    Kroo, I.M.2    Jameson, A.3
  • 3
    • 21344492353 scopus 로고
    • Fast plane rotations with dynamic scaling
    • A. Anda and H. Park, "Fast plane rotations with dynamic scaling." SIAM J. Matrix Anal. Appl. 15:162-174, 1994.
    • (1994) SIAM J. Matrix Anal. Appl. , vol.15 , pp. 162-174
    • Anda, A.1    Park, H.2
  • 6
    • 0000369555 scopus 로고
    • An improved algorithm for discrete -1 linear approximation
    • I. Barrodale and F. D. K. Roberts, "An improved algorithm for discrete -1 linear approximation." SIAM J. Numer. Anal. 10:839-848, 1973.
    • (1973) SIAM J. Numer. Anal. , vol.10 , pp. 839-848
    • Barrodale, I.1    Roberts, F.D.K.2
  • 8
    • 0016061478 scopus 로고
    • The fitting of power series, meaning polynomials, illustrated on band-spectroscopic data
    • A. E. Beaton and J. W. Tukey, "The fitting of power series, meaning polynomials, illustrated on band-spectroscopic data." Technometrics 16:147-185, 1974.
    • (1974) Technometrics , vol.16 , pp. 147-185
    • Beaton, A.E.1    Tukey, J.W.2
  • 10
    • 0017958142 scopus 로고
    • Asynchronous iterative methods for multiprocessors
    • G. M. Baudet, "Asynchronous iterative methods for multiprocessors." J. ACM 15:226-244, 1978.
    • (1978) J. ACM , vol.15 , pp. 226-244
    • Baudet, G.M.1
  • 11
    • 34247386378 scopus 로고    scopus 로고
    • Finding a global optimal solution for a quadratically constrained fractional quadratic problem with applications to the regularized total least squares
    • A. Beck, A. Ben-Tal and M. Teboulle, "Finding a global optimal solution for a quadratically constrained fractional quadratic problem with applications to the regularized total least squares." SIAM J. Matrix Anal. Appl. 28:425-445, 2006.
    • (2006) SIAM J. Matrix Anal. Appl. , vol.28 , pp. 425-445
    • Beck, A.1    Ben-Tal, A.2    Teboulle, M.3
  • 12
    • 0002741413 scopus 로고
    • Large scale sparse singular value computations
    • M. Berry, "Large scale sparse singular value computations." International J. Supercomp. Appl. 6:13-49, 1992.
    • (1992) International J. Supercomp. Appl. , vol.6 , pp. 13-49
    • Berry, M.1
  • 14
    • 0032083715 scopus 로고    scopus 로고
    • Computing rank-revealing qr factorization of dense matrices
    • C. H. Bischof and G. Qintana-Orti, "Computing rank-revealing QR factorization of dense matrices." ACM TOMS 24:226-253, 1998.
    • (1998) ACM TOMS , vol.24 , pp. 226-253
    • Bischof, C.H.1    Qintana-Orti, G.2
  • 16
    • 0002168778 scopus 로고
    • Solving linear least squares problems by gram-schmidt orthogonalization
    • Å. Björck, "Solving linear least squares problems by Gram-Schmidt orthogonalization." BIT 7:1-21, 1967.
    • (1967) BIT , vol.7 , pp. 1-21
    • Björck Å.1
  • 17
    • 0001473420 scopus 로고
    • Iterative refinement of linear least squares solutions
    • Å. Björck, "Iterative refinement of linear least squares solutions." BIT 7:257-278, 1967.
    • (1967) BIT , vol.7 , pp. 257-278
    • Björck Å.1
  • 18
    • 0002961792 scopus 로고
    • Iterative refinement of linear least squares solutions II
    • Å. Björck, "Iterative refinement of linear least squares solutions II." BIT 8:8-30, 1968.
    • (1968) BIT , vol.8 , pp. 8-30
    • Björck Å.1
  • 19
    • 0002671024 scopus 로고
    • Stability analysis of the method of seminormal equations for linear least squares problems
    • Å. Björck, "Stability analysis of the method of seminormal equations for linear least squares problems." Lin. Alg. Appl. 88/89:31-48, 1987.
    • (1987) Lin. Alg. Appl. , vol.88-89 , pp. 31-48
    • Björck Å.1
  • 21
    • 18144440986 scopus 로고    scopus 로고
    • The calculation of linear least squares problems
    • Å. Björck, "The calculation of linear least squares problems." Acta Numerica 13:1-53, 2004.
    • (2004) Acta Numerica , vol.13 , pp. 1-53
    • Björck Å.1
  • 22
    • 0001786995 scopus 로고
    • A direct method for the solution of sparse linear least squares problems
    • Å. Björck and I. S. Duff, "A direct method for the solution of sparse linear least squares problems." Lin. Alg. Appl. 34:43-67, 1980.
    • (1980) Lin. Alg. Appl. , vol.34 , pp. 43-67
    • Björck Å.1    Duff, I.S.2
  • 23
    • 0001473421 scopus 로고
    • Iterative refinement of linear least squares solution by householder transformation
    • Å. Björck and G. H. Golub, "Iterative refinement of linear least squares solution by Householder transformation." BIT 7:322-337, 1967.
    • (1967) BIT , vol.7 , pp. 322-337
    • Björck Å.1    Golub, G.H.2
  • 24
    • 0001765884 scopus 로고
    • An implicit shift bidiagonalization algorithm for ill-posed systems
    • Å. Björck, E. Grimme and P. Van Dooren, "An implicit shift bidiagonalization algorithm for ill-posed systems." BIT 34:510-534, 1994.
    • (1994) BIT , vol.34 , pp. 510-534
    • Björck Å.1    Grimme, E.2    Van Dooren, P.3
  • 26
    • 0001688779 scopus 로고
    • Loss and recapture of orthogonality in the modified gram-schmidt algorithm
    • Å. Björck and C. C. Paige, "Loss and recapture of orthogonality in the modified Gram-Schmidt algorithm." SIAM J. Matrix Anal. 13:176- 190, 1992.
    • (1992) SIAM J. Matrix Anal. , vol.13 , pp. 176-190
    • Björck Å.1    Paige, C.C.2
  • 27
    • 84968468488 scopus 로고
    • Solution of vandermonde systems of equations
    • Å. Björck and V. Pereyra, "Solution of Vandermonde systems of equations." Math. Comp. 24:893-904, 1970.
    • (1970) Math. Comp. , vol.24 , pp. 893-904
    • Björck Å.1    Pereyra, V.2
  • 28
    • 0013019284 scopus 로고
    • A modification of the trust-region gauss-newton method for separable nonlinear least squares problems
    • C. Böckman, "A modification of the trust-region Gauss-Newton method for separable nonlinear least squares problems." J. Math. Systems, Estimation and Control 5:1-16, 1995.
    • (1995) J. Math. Systems, Estimation and Control , vol.5 , pp. 1-16
    • Böckman, C.1
  • 29
    • 24944585477 scopus 로고
    • A practical guide to splines
    • Springer, New York
    • C. de Boor, A Practical Guide to Splines. Applied Mathematical Sciences 27. Springer, New York, 1994.
    • (1994) Applied Mathematical Sciences , vol.27
    • De Boor, C.1
  • 31
  • 33
    • 0000924088 scopus 로고    scopus 로고
    • Estimation of the l-curve via lanczos bidiagonalization algorithm for ill-posed systems
    • D. Calvetti, G. H. Golub and L. Reichel, "Estimation of the L-curve via Lanczos bidiagonalization algorithm for ill-posed systems." BIT 39:603-619, 1999.
    • (1999) BIT , vol.39 , pp. 603-619
    • Calvetti, D.1    Golub, G.H.2    Reichel, L.3
  • 35
    • 85032750937 scopus 로고    scopus 로고
    • People hearing without listening: An introduction to compressive sampling
    • IEEE
    • E. J. Candes and M. B. Wakin, "People hearing without listening: An introduction to compressive sampling." Signal Processing Magazine, IEEE 25:21-30, 2008.
    • (2008) Signal Processing Magazine , vol.25 , pp. 21-30
    • Candes, E.J.1    Wakin, M.B.2
  • 40
    • 0002170151 scopus 로고
    • Rank revealing qr-factorizations
    • T. F. Chan, "Rank revealing QR-factorizations." Lin. Alg. Appl. 88/89:67-82, 1987.
    • (1987) Lin. Alg. Appl. , vol.88-89 , pp. 67-82
    • Chan, T.F.1
  • 41
    • 0012096192 scopus 로고
    • Effectively well-conditioned linear systems
    • T. F. Chan and D. E. Foulser, "Effectively well-conditioned linear systems." SIAM J. Sci. Stat. Comput. 9:963-969, 1988.
    • (1988) SIAM J. Sci. Stat. Comput. , vol.9 , pp. 963-969
    • Chan, T.F.1    Foulser, D.E.2
  • 42
    • 0001138266 scopus 로고
    • Computing truncated SVD least squares solutions by rank revealing QR-factorizations
    • T. F. Chan and P. C. Hansen, "Computing truncated SVD least squares solutions by rank revealing QR-factorizations." SIAM J. Sci. Statist. Comput. 11:519-530, 1991.
    • (1991) SIAM J. Sci. Statist. Comput. , vol.11 , pp. 519-530
    • Chan, T.F.1    Hansen, P.C.2
  • 46
    • 85067317817 scopus 로고    scopus 로고
    • Supersonic business jet design using knowledge-based genetic algorithms with adaptive, unstructured grid methodology
    • AIAA 2003-3791, Orlando, Fl. June
    • H. S. Chung, S. Choi and J. J. Alonso, "Supersonic business jet design using knowledge-based genetic algorithms with adaptive, unstructured grid methodology." AIAA 2003-3791, 21st Applied Aerodynamic Conference, Orlando, Fl., June 2003.
    • (2003) 21st Applied Aerodynamic Conference
    • Chung, H.S.1    Choi, S.2    Alonso, J.J.3
  • 48
    • 0000364765 scopus 로고
    • Robust modeling with erratic data
    • J. F. Claerbout and F. Muir, "Robust modeling with erratic data." Geophysics 38:826-844, 1973.
    • (1973) Geophysics , vol.38 , pp. 826-844
    • Claerbout, J.F.1    Muir, F.2
  • 49
    • 0012064863 scopus 로고
    • An elimination method for the solution of linear least squares problems
    • A. K. Cline, "An elimination method for the solution of linear least squares problems." SIAM J. Numer. Anal. 10:283-289, 1973.
    • (1973) SIAM J. Numer. Anal. , vol.10 , pp. 283-289
    • Cline, A.K.1
  • 50
    • 84907772436 scopus 로고
    • A system of subroutines for iteratively reweighted least squares computations
    • D. Coleman, P. Holland, N. Kaden, V. Klema and S. C. Peters, "A system of subroutines for iteratively reweighted least squares computations." ACM TOMS 6:328-336, 1980.
    • (1980) ACM TOMS , vol.6 , pp. 328-336
    • Coleman, D.1    Holland, P.2    Kaden, N.3    Klema, V.4    Peters, S.C.5
  • 51
    • 34249840880 scopus 로고
    • A globally and quadratically convergent affine scaling method for linear -1 problems
    • Series A
    • T. F. Coleman and Y. Li, "A globally and quadratically convergent affine scaling method for linear -1 problems." Mathematical Programming, Series A 56:189-222, 1992.
    • (1992) Mathematical Programming , vol.56 , pp. 189-222
    • Coleman, T.F.1    Li, Y.2
  • 53
    • 78651578861 scopus 로고    scopus 로고
    • Parallel scientific computing on loosely coupled networks of computers
    • B. Koren and C. Vuik, editors, Springer Series Lecture Notes in Computational Science and Engineering, Springer Verlag, Berlin/Heidelberg, Germany
    • T. P. Collignon and M. B. van Gijzen. "Parallel scientific computing on loosely coupled networks of computers." In B. Koren and C. Vuik, editors, Advanced Computational Methods in Science and Engineering. Springer Series Lecture Notes in Computational Science and Engineering, 71:79-106. Springer Verlag, Berlin/Heidelberg, Germany, 2010.
    • (2010) Advanced Computational Methods in Science and Engineering , vol.71 , pp. 79-106
    • Collignon, T.P.1    Van Gijzen, M.B.2
  • 54
    • 0024861871 scopus 로고
    • Approximation by superpositions of a sigmoidal function
    • G. Cybenko, "Approximation by superpositions of a sigmoidal function." Math. Control Signals Systems 2:303-314, 1989.
    • (1989) Math. Control Signals Systems , vol.2 , pp. 303-314
    • Cybenko, G.1
  • 55
    • 77952545420 scopus 로고    scopus 로고
    • Algorithms and software for total variation image reconstruction via first-order methods
    • J. Dahl, P. C. Hansen, S. H. Jensen and T. L. Jensen, "Algorithms and software for total variation image reconstruction via first-order methods." Numer. Algo. 53:67-92, 2010.
    • (2010) Numer. Algo. , vol.53 , pp. 67-92
    • Dahl, J.1    Hansen, P.C.2    Jensen, S.H.3    Jensen, T.L.4
  • 58
    • 81355161778 scopus 로고    scopus 로고
    • The university of florida sparse matrix collection
    • T. A. Davis and Y. Hu, "The University of Florida sparse matrix collection." ACM TOMS 38:1-25, 2011.
    • (2011) ACM TOMS , vol.38 , pp. 1-25
    • Davis, T.A.1    Hu, Y.2
  • 60
    • 0026238244 scopus 로고
    • The bidiagonal singular value decomposition and hamiltonian mechanics
    • P. Deift, J. Demmel, L.-C. Li and C. Tomei, "The bidiagonal singular value decomposition and Hamiltonian mechanics." SIAM J. Numer. Anal. 28:1463-1516, 1991.
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 1463-1516
    • Deift, P.1    Demmel, J.2    Li, L.-C.3    Tomei, C.4
  • 62
    • 0024875017 scopus 로고
    • Fast least squares solution of vandermonde systems of equations
    • C. J. Demeure and L. L. Scharf, "Fast least squares solution of Vandermonde systems of equations." Acoustics, Speech and Signal Processing 4:2198-2210, 1989.
    • (1989) Acoustics, Speech and Signal Processing , vol.4 , pp. 2198-2210
    • Demeure, C.J.1    Scharf, L.L.2
  • 64
    • 61349142482 scopus 로고    scopus 로고
    • Extra-precise iterative refinement for overdetermined least squares problems
    • J. Demmel, Y. Hida, W. Riedy and X. S. Li, "Extra-precise iterative refinement for overdetermined least squares problems." ACM TOMS 35:1-32, 2009.
    • (2009) ACM TOMS , vol.35 , pp. 1-32
    • Demmel, J.1    Hida, Y.2    Riedy, W.3    Li, X.S.4
  • 65
    • 84976747891 scopus 로고
    • Algorithm 573 NL2SOL - An adaptive nonlinear least-squares algorithm
    • J. Dennis, D. M. Gay and R. Welsch, "Algorithm 573 NL2SOL - An adaptive nonlinear least-squares algorithm." ACM TOMS 7:369-383, 1981.
    • (1981) ACM TOMS , vol.7 , pp. 369-383
    • Dennis, J.1    Gay, D.M.2    Welsch, R.3
  • 67
    • 0000947761 scopus 로고
    • Convergence theorems for leastchange secant update methods
    • J. E. Dennis and H. F. Walker, "Convergence theorems for leastchange secant update methods." SIAM J. Num. Anal. 18:949-987, 1981.
    • (1981) SIAM J. Num. Anal. , vol.18 , pp. 949-987
    • Dennis, J.E.1    Walker, H.F.2
  • 72
    • 0000802374 scopus 로고
    • The approximation of one matrix by another of lower rank
    • C. Eckart and G. Young, "The approximation of one matrix by another of lower rank." Psychometrika 1:211-218, 1936.
    • (1936) Psychometrika , vol.1 , pp. 211-218
    • Eckart, C.1    Young, G.2
  • 73
    • 0002626762 scopus 로고
    • A note on the computation of the generalized crossvalidation function for ill-conditioned least squares problems
    • L. Eldén, "A note on the computation of the generalized crossvalidation function for ill-conditioned least squares problems." BIT 24:467-472, 1984.
    • (1984) BIT , vol.24 , pp. 467-472
    • Eldén, L.1
  • 74
    • 0001152877 scopus 로고
    • Perturbation theory for the linear least squares problem with linear equality constraints
    • L. Eldén, "Perturbation theory for the linear least squares problem with linear equality constraints." BIT 17:338-350, 1980.
    • (1980) BIT , vol.17 , pp. 338-350
    • Eldén, L.1
  • 77
    • 10044265544 scopus 로고    scopus 로고
    • Truncated gauss-newton algorithms for ill-conditioned nonlinear least squares problems
    • J. Eriksson and P.-Å. Wedin, "Truncated Gauss-Newton algorithms for ill-conditioned nonlinear least squares problems." Optimiz. Meth. and Software 19:721-737, 2004.
    • (2004) Optimiz. Meth. and Software , vol.19 , pp. 721-737
    • Eriksson, J.1    Wedin P.-Å.2
  • 78
    • 0033423414 scopus 로고    scopus 로고
    • UTV tools: MATLAB templates for rank-revealing utv decompositions
    • The software is available from
    • R. D. Fierro, P. C. Hansen and P. S. K. Hansen, "UTV tools: MATLAB templates for rank-revealing UTV decompositions." Numer. Algo. 20:165-194, 1999. The software is available from: htpp://www.netlib.org/numeralgo.
    • (1999) Numer. Algo. , vol.20 , pp. 165-194
    • Fierro, R.D.1    Hansen, P.C.2    Hansen, P.S.K.3
  • 79
    • 1642633428 scopus 로고    scopus 로고
    • Second edition Brooks/Cole, Belmont, CA
    • P. M. Fitzpatrick, Advanced Calculus. Second edition Brooks/Cole, Belmont, CA, 2006.
    • (2006) Advanced Calculus
    • Fitzpatrick, P.M.1
  • 80
    • 81555200713 scopus 로고    scopus 로고
    • LSMR: An iterative algorithm for sparse least-squares problems
    • D. Fong and M. A. Saunders, "LSMR: An iterative algorithm for sparse least-squares problems." SIAM J. Sci. Comput. 33:2950-2971, 2011.
    • (2011) SIAM J. Sci. Comput. , vol.33 , pp. 2950-2971
    • Fong, D.1    Saunders, M.A.2
  • 81
    • 0002099734 scopus 로고
    • Generation and use of orthogonal polynomials for data-fitting with a digital computer
    • G. E. Forsythe, "Generation and use of orthogonal polynomials for data-fitting with a digital computer." J. SIAM 5:74-88, 1957.
    • (1957) J. SIAM , vol.5 , pp. 74-88
    • Forsythe, G.E.1
  • 85
    • 84907785291 scopus 로고
    • Tradeoffs in algorithms for separable nonlinear least squares
    • D. M. Gay and L. Kaufman, Tradeoffs in Algorithms for Separable Nonlinear Least Squares. AT&T Bell Labs. Num. Anal. Manuscript, 90-11, 1990.
    • (1990) AT&T Bell Labs. Num. Anal. Manuscript , vol.90 , Issue.11
    • Gay, D.M.1    Kaufman, L.2
  • 88
    • 0003658224 scopus 로고
    • Users guide for lssol (version 1.0): A Fortran package for constrained linear least-squares and convex quadratic programming
    • Stanford University, CA
    • P. E. Gill, S. J. Hammarling, W. Murray, M. A. Saunders and M. H. Wright, Users Guide for LSSOL (Version 1.0): A Fortran Package for Constrained Linear Least-Squares and Convex Quadratic Programming. Report 86-1 Department of Operation Research, Stanford University, CA, 1986.
    • (1986) Report Department of Operation Research
    • Gill, P.E.1    Hammarling, S.J.2    Murray, W.3    Saunders, M.A.4    Wright, M.H.5
  • 89
    • 17444372724 scopus 로고    scopus 로고
    • SNOPT: An SQP algorithm for large-scale constrained optimization
    • P. E. Gill, W. Murray and M. A. Saunders, "SNOPT: An SQP algorithm for large-scale constrained optimization." SIAM Rev. 47:99- 131, 2005.
    • (2005) SIAM Rev. , vol.47 , pp. 99-131
    • Gill, P.E.1    Murray, W.2    Saunders, M.A.3
  • 92
    • 0000924593 scopus 로고
    • Numerical methods for solving linear least squares problems
    • G. H. Golub, "Numerical methods for solving linear least squares problems." Numer. Math. 7:206-16, 1965.
    • (1965) Numer. Math. , vol.7 , pp. 206-216
    • Golub, G.H.1
  • 94
    • 32044449925 scopus 로고
    • Generalized cross-validation as a method for choosing a good ridge parameter
    • G. H. Golub, M. Heath and G. Wahba, "Generalized cross-validation as a method for choosing a good ridge parameter." Technometrics 21:215-223, 1979.
    • (1979) Technometrics , vol.21 , pp. 215-223
    • Golub, G.H.1    Heath, M.2    Wahba, G.3
  • 95
    • 45949115772 scopus 로고
    • A generalization of the eckhard-young-mirsky matrix approximation theorem
    • G. H. Golub, A. Hoffman and G. W. Stewart, "A generalization of the Eckhard-Young-Mirsky matrix approximation theorem." Linear Algebra Appl. 88/89:317-327, 1987.
    • (1987) Linear Algebra Appl. , vol.88-89 , pp. 317-327
    • Golub, G.H.1    Hoffman, A.2    Stewart, G.W.3
  • 96
    • 0000288016 scopus 로고
    • Calculating the singular values and pseudo-inverse of a matrix
    • G. H. Golub and W. Kahan, "Calculating the singular values and pseudo-inverse of a matrix." SIAM J, Numer. Anal. Ser. B 2:205- 224, 1965.
    • (1965) SIAM J, Numer. Anal. Ser. B , vol.2 , pp. 205-224
    • Golub, G.H.1    Kahan, W.2
  • 98
    • 0003072966 scopus 로고
    • Extensions and uses of the variable projection algorithm for solving nonlinear least squares problems
    • White Sands Missile Range, New Mexico
    • G. H. Golub and R. Le Veque, "Extensions and uses of the variable projection algorithm for solving nonlinear least squares problems." Proceedings of the Army Numerical Analysis and Computers Conference, White Sands Missile Range, New Mexico, pp. 1-12, 1979.
    • (1979) Proceedings of the Army Numerical Analysis and Computers Conference , pp. 1-12
    • Golub, G.H.1    Le Veque, R.2
  • 99
    • 0040354352 scopus 로고    scopus 로고
    • Tikhonov regularization for large problems
    • Ed. G. H. Golub, S. H. Lui, F. Luk and R. Plemmons, Springer, New York
    • G. H. Golub and U. von Matt, "Tikhonov regularization for large problems." Workshop on Scientific Computing, Ed. G. H. Golub, S. H. Lui, F. Luk and R. Plemmons, Springer, New York, 1997.
    • (1997) Workshop on Scientific Computing
    • Golub, G.H.1    Von Matt, U.2
  • 101
    • 0000803444 scopus 로고
    • The differentiation of pseudo-inverses and nonlinear least squares problems whose variables separate
    • G. H. Golub and V. Pereyra, "The differentiation of pseudo-inverses and nonlinear least squares problems whose variables separate." SIAM J. Numer. Anal. 10:413-432, 1973.
    • (1973) SIAM J. Numer. Anal. , vol.10 , pp. 413-432
    • Golub, G.H.1    Pereyra, V.2
  • 102
    • 84907761984 scopus 로고
    • Differentiation of pseudoinverses, separable nonlinear least squares problems, and other tales
    • Ed. Z. Nashed, Academic Press, NY
    • G. H. Golub and V. Pereyra, "Differentiation of pseudoinverses, separable nonlinear least squares problems, and other tales." Proceedings MRC Seminar on Generalized Inverses and Their Applications, Ed. Z. Nashed, pp. 302-324, Academic Press, NY, 1976.
    • (1976) Proceedings MRC Seminar on Generalized Inverses and their Applications , pp. 302-324
    • Golub, G.H.1    Pereyra, V.2
  • 103
    • 0037390670 scopus 로고    scopus 로고
    • Separable nonlinear least squares: The variable projection method and its applications
    • G. H. Golub and V. Pereyra, "Separable nonlinear least squares: The variable projection method and its applications." Inverse Problems 19:R1-R26, 2003.
    • (2003) Inverse Problems , vol.19 , pp. R1-R26
    • Golub, G.H.1    Pereyra, V.2
  • 104
    • 0016073097 scopus 로고
    • On a characterization of the best -2-scaling of a matrix
    • G. H. Golub and J. M. Varah, "On a characterization of the best -2-scaling of a matrix." SIAM J. Numer. Anal. 11:472-279, 1974.
    • (1974) SIAM J. Numer. Anal. , vol.11 , pp. 279-472
    • Golub, G.H.1    Varah, J.M.2
  • 105
    • 0004236492 scopus 로고    scopus 로고
    • Third edition, John Hopkins University Press, Baltimore
    • G. H. Golub and C. F. Van Loan, Matrix Computations. Third edition, John Hopkins University Press, Baltimore, 1996.
    • (1996) Matrix Computations
    • Golub, G.H.1    Van Loan, C.F.2
  • 106
    • 0000333571 scopus 로고
    • An analysis of the total least squares problem
    • G. H. Golub and C. F. Van Loan, "An analysis of the total least squares problem." SIAM J. Numer. Anal. 17:883-893, 1980.
    • (1980) SIAM J. Numer. Anal. , vol.17 , pp. 883-893
    • Golub, G.H.1    Van Loan, C.F.2
  • 107
    • 0012096207 scopus 로고
    • Note on iterative refinement of least squares solutions
    • G. H. Golub and J. H. Wilkinson, "Note on iterative refinement of least squares solutions." Numer. Math. 9:139-148, 1966.
    • (1966) Numer. Math. , vol.9 , pp. 139-148
    • Golub, G.H.1    Wilkinson, J.H.2
  • 109
    • 79959868916 scopus 로고    scopus 로고
    • Mathematicians of gaussian elimination
    • J. F. Grcar, "Mathematicians of Gaussian elimination." Notices of the AMS 58:782-792, 2011.
    • (2011) Notices of the AMS , vol.58 , pp. 782-792
    • Grcar, J.F.1
  • 110
    • 79959906956 scopus 로고    scopus 로고
    • John von Neumann's analysis of gaussian elimination and the origins of modern numerical analysis
    • J. F. Grcar, "John von Neumann's analysis of Gaussian elimination and the origins of modern Numerical Analysis." SIAM Review 53:607-682, 2011.
    • (2011) SIAM Review , vol.53 , pp. 607-682
    • Grcar, J.F.1
  • 111
    • 77953225791 scopus 로고    scopus 로고
    • Evaluating derivatives: Principles and techniques of algorithmic differentiation
    • Second edition, SIAM, Philadelphia
    • A. Griewank and A. Walther, Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation. Other Titles in Applied Mathematics 105. Second edition, SIAM, Philadelphia, 2008.
    • (2008) Other Titles in Applied Mathematics , vol.105
    • Griewank, A.1    Walther, A.2
  • 112
    • 1542484176 scopus 로고
    • Tensor spline approximation
    • E. Grosse, "Tensor spline approximation." Linear Algebra Appl. 34:29-41, 1980.
    • (1980) Linear Algebra Appl. , vol.34 , pp. 29-41
    • Grosse, E.1
  • 113
    • 0001652904 scopus 로고
    • Least squares estimation for a class of nonlinear models
    • I. Gutman, V. Pereyra and H. D. Scolnik, "Least squares estimation for a class of nonlinear models." Technometrics 15:209-218, 1973.
    • (1973) Technometrics , vol.15 , pp. 209-218
    • Gutman, I.1    Pereyra, V.2    Scolnik, H.D.3
  • 114
    • 0015094608 scopus 로고
    • On a bicriterion formulation of the problem of integrated system identification and system optimization
    • Y. Y. Haimes, L. S. Ladon and D. A. Wismer, "On a bicriterion formulation of the problem of integrated system identification and system optimization." IEEE Trans. on Systems, Man and Cybernetics 1:296-297, 1971.
    • (1971) IEEE Trans. on Systems, Man and Cybernetics , vol.1 , pp. 296-297
    • Haimes, Y.Y.1    Ladon, L.S.2    Wismer, D.A.3
  • 115
    • 0012095290 scopus 로고
    • A note on modifications to the givens plane rotations
    • S. Hammarling, "A note on modifications to the Givens plane rotations." J. Inst. Math. Applic. 13:215-218, 1974.
    • (1974) J. Inst. Math. Applic. , vol.13 , pp. 215-218
    • Hammarling, S.1
  • 117
    • 0001273835 scopus 로고
    • Regularization methods for large-scale problems
    • M. Hanke and P. C. Hansen, "Regularization methods for large-scale problems." Surv. Math. Ind. 3:253-315, 1993.
    • (1993) Surv. Math. Ind. , vol.3 , pp. 253-315
    • Hanke, M.1    Hansen, P.C.2
  • 118
    • 0003235718 scopus 로고    scopus 로고
    • Rank-deficient and discrete Ill-posed problems
    • Philadelphia
    • P. C. Hansen, Rank-Deficient and Discrete Ill-Posed Problems. SIAM, Philadelphia, 1998.
    • (1998) SIAM
    • Hansen, P.C.1
  • 119
    • 0000236333 scopus 로고    scopus 로고
    • The l-curve and its use in the numerical treatment of inverse problems
    • Ed. P. Johnston, WIT Press, Southampton, UK
    • P. C. Hansen, "The L-curve and its use in the numerical treatment of inverse problems." In Comp. Inverse Problems in Electrocardiology. Ed. P. Johnston, pp. 119-142, WIT Press, Southampton, UK, 2001.
    • (2001) Comp. Inverse Problems in Electrocardiology , pp. 119-142
    • Hansen, P.C.1
  • 120
    • 36448976249 scopus 로고    scopus 로고
    • Regularization tools version 4.0 for matlab 7.3
    • P. C. Hansen, "Regularization tools version 4.0 for MATLAB 7.3." Numer. Algorithms 46:189-194, 2007.
    • (2007) Numer. Algorithms , vol.46 , pp. 189-194
    • Hansen, P.C.1
  • 121
    • 84878323336 scopus 로고    scopus 로고
    • Discrete inverse problems - insight and algorithms
    • Philadelphia
    • P. C. Hansen, Discrete Inverse Problems - Insight and Algorithms. SIAM, Philadelphia, 2010.
    • (2010) SIAM
    • Hansen, P.C.1
  • 122
    • 33645036956 scopus 로고    scopus 로고
    • Exploiting residual information in the parameter choice for discrete ill-posed problems
    • P. C. Hansen, M. Kilmer and R. H. Kjeldsen, "Exploiting residual information in the parameter choice for discrete ill-posed problems." BIT 46:41-59, 2006.
    • (2006) BIT , vol.46 , pp. 41-59
    • Hansen, P.C.1    Kilmer, M.2    Kjeldsen, R.H.3
  • 123
    • 84855521659 scopus 로고    scopus 로고
    • Air tools - A matlab package of algebraic iterative reconstruction methods
    • P. C. Hansen and M. Saxild-Hansen, "AIR tools - A MATLAB package of algebraic iterative reconstruction methods." J. Comp. Appl. Math. 236:2167-2178, 2011.
    • (2011) J. Comp. Appl. Math. , vol.236 , pp. 2167-2178
    • Hansen, P.C.1    Saxild-Hansen, M.2
  • 124
    • 0036056544 scopus 로고    scopus 로고
    • Computing symmetric rank-revealing decompositions via triangular factorization
    • P. C. Hansen and P. Yalamov, "Computing symmetric rank-revealing decompositions via triangular factorization." SIAM J. Matrix Anal. Appl. 23:443-458, 2001.
    • (2001) SIAM J. Matrix Anal. Appl. , vol.23 , pp. 443-458
    • Hansen, P.C.1    Yalamov, P.2
  • 126
    • 0000135303 scopus 로고
    • Methods of conjugate gradients for solving linear systems
    • M. R. Hestenes and E. Stiefel, "Methods of conjugate gradients for solving linear systems." J. Res. Nat. Stan. B. 49:409-432, 1952.
    • (1952) J. Res. Nat. Stan. B. , vol.49 , pp. 409-432
    • Hestenes, M.R.1    Stiefel, E.2
  • 127
    • 0003306408 scopus 로고
    • Analysis of the cholesky decomposition of a semi-definite matrix
    • ed. M. G. Cox and S. J. Hammarling, Oxford University Press, London
    • N. Higham, "Analysis of the Cholesky decomposition of a semi-definite matrix." In Reliable Numerical Computing, ed. M. G. Cox and S. J. Hammarling, Oxford University Press, London, 1990.
    • (1990) Reliable Numerical Computing
    • Higham, N.1
  • 129
    • 84968501766 scopus 로고
    • Rank-revealing qr factorization and svd
    • H. P. Hong and C. T. Pan, "Rank-revealing QR factorization and SVD." Math. Comp. 58:213-232, 1992.
    • (1992) Math. Comp. , vol.58 , pp. 213-232
    • Hong, H.P.1    Pan, C.T.2
  • 132
    • 23044525261 scopus 로고    scopus 로고
    • Multiple imputation in practice: Comparison of software packages for regression models with missing variables
    • N. J. Horton and S. R. Lipsitz, "Multiple imputation in practice: Comparison of software packages for regression models with missing variables." The American Statistician 55, 2011.
    • (2011) The American Statistician , vol.55
    • Horton, N.J.1    Lipsitz, S.R.2
  • 133
    • 0032280255 scopus 로고    scopus 로고
    • The idea behind krylov methods
    • I. C. F. Ipsen and C. D. Meyer, "The idea behind Krylov methods." Amer. Math. Monthly 105:889-899, 1998.
    • (1998) Amer. Math. Monthly , vol.105 , pp. 889-899
    • Ipsen, I.C.F.1    Meyer, C.D.2
  • 136
    • 84968515140 scopus 로고
    • Experiments on error growth associated with some linear least squares procedures
    • T. L. Jordan, "Experiments on error growth associated with some linear least squares procedures." Math. Comp. 22:579-588, 1968.
    • (1968) Math. Comp. , vol.22 , pp. 579-588
    • Jordan, T.L.1
  • 137
    • 33747818869 scopus 로고
    • Approximation to data by splines with free knots
    • D. L. Jupp, "Approximation to data by splines with free knots." SIAM J. Numer. Anal. 15:328, 1978.
    • (1978) SIAM J. Numer. Anal. , vol.15 , pp. 328
    • Jupp, D.L.1
  • 138
    • 10844223923 scopus 로고
    • Stable iterative methods for the inversion of geophysical data
    • D. L. Jupp and K. Vozoff, "Stable iterative methods for the inversion of geophysical data." J. R. Astr. Soc. 42:957-976, 1975.
    • (1975) J. R. Astr. Soc. , vol.42 , pp. 957-976
    • Jupp, D.L.1    Vozoff, K.2
  • 140
    • 0016450838 scopus 로고
    • A variable projection method for solving nonlinear least squares problems
    • L. Kaufman, "A variable projection method for solving nonlinear least squares problems." BIT 15:49-57, 1975.
    • (1975) BIT , vol.15 , pp. 49-57
    • Kaufman, L.1
  • 141
    • 0002280491 scopus 로고
    • Separable nonlinear least squares with multiple right-hand sides
    • L. Kaufman and G. Sylvester, "Separable nonlinear least squares with multiple right-hand sides." SIAM J. Matrix Anal. and Appl. 13:68- 89, 1992.
    • (1992) SIAM J. Matrix Anal. and Appl. , vol.13 , pp. 68-89
    • Kaufman, L.1    Sylvester, G.2
  • 142
    • 0013017015 scopus 로고
    • A method for separable nonlinear least squares problems with separable equality constraints
    • L. Kaufman and V. Pereyra, "A method for separable nonlinear least squares problems with separable equality constraints." SIAM J. Numer. Anal. 15:12-20, 1978.
    • (1978) SIAM J. Numer. Anal. , vol.15 , pp. 12-20
    • Kaufman, L.1    Pereyra, V.2
  • 144
    • 0035537408 scopus 로고    scopus 로고
    • Choosing regularization parameters in iterative methods for ill-posed problems
    • M. E. Kilmer and D. P. O'Leary, "Choosing regularization parameters in iterative methods for ill-posed problems." SIAM. J. Matrix Anal. Appl. 22:1204-1221, 2001.
    • (2001) SIAM. J. Matrix Anal. Appl. , vol.22 , pp. 1204-1221
    • Kilmer, M.E.1    O'Leary, D.P.2
  • 145
    • 14044276332 scopus 로고    scopus 로고
    • Missing value estimation for dna microarray expression data: Least squares imputation
    • Stanford, CA
    • H. Kim, G. H. Golub and H. Park, "Missing value estimation for DNA microarray expression data: Least squares imputation." In Proceedings of CSB'2004, Stanford, CA, pp. 572-573, 2004.
    • (2004) Proceedings of CSB'2004 , pp. 572-573
    • Kim, H.1    Golub, G.H.2    Park, H.3
  • 147
    • 0003028425 scopus 로고
    • Nonlinear programming
    • University of California Press, Berkeley
    • H. W. Kuhn and A. W. Tucker, Nonlinear Programming. Proceedings of 2nd Berkeley Symposium, 481-492, University of California Press, Berkeley, 1951.
    • (1951) Proceedings of 2nd Berkeley Symposium , pp. 481-492
    • Kuhn, H.W.1    Tucker, A.W.2
  • 151
    • 0000873069 scopus 로고
    • A method for the solution of certain nonlinear problems in least squares
    • K. Levenberg, "A method for the solution of certain nonlinear problems in least squares." Quart. J. App. Math. 2:164-168, 1948.
    • (1948) Quart. J. App. Math. , vol.2 , pp. 164-168
    • Levenberg, K.1
  • 153
    • 0000024127 scopus 로고
    • A finite smoothing algorithm for linear -1 estimation
    • K. Madsen and H. B. Nielsen, "A finite smoothing algorithm for linear -1 estimation." SIAM J. Optimiz. 3:223-235, 1993.
    • (1993) SIAM J. Optimiz. , vol.3 , pp. 223-235
    • Madsen, K.1    Nielsen, H.B.2
  • 154
    • 84907715907 scopus 로고    scopus 로고
    • Lecture notes, Informatics and Mathematical Modelling, Technical University of Denmark, Lyngby
    • K. Madsen and H. B. Nielsen, Introduction to Optimization and Data Fitting. Lecture notes, Informatics and Mathematical Modelling, Technical University of Denmark, Lyngby, 2008.
    • (2008) Introduction to Optimization and Data Fitting
    • Madsen, K.1    Nielsen, H.B.2
  • 155
    • 34249825770 scopus 로고    scopus 로고
    • Overview of total least-squares methods
    • I. Markovsky and S. Van Huffel, "Overview of total least-squares methods." Signal Processsing 87:2283-2302, 2007.
    • (2007) Signal Processsing , vol.87 , pp. 2283-2302
    • Markovsky, I.1    Van Huffel, S.2
  • 156
    • 84957764500 scopus 로고    scopus 로고
    • Master's Thesis, Stanford University, Stanford, CA
    • O. Mate, "Missing value problem." Master's Thesis, Stanford University, Stanford, CA, 2007.
    • (2007) Missing Value Problem
    • Mate, O.1
  • 157
    • 20344394051 scopus 로고    scopus 로고
    • Matrix Market. http://math.nist.gov/MatrixMarket.
    • Matrix Market
  • 159
    • 0009403782 scopus 로고
    • Iterations chaotiques a retards
    • J.-C. Miellou, "Iterations chaotiques a retards." C. R. Acad. Sci. Paris 278:957-960, 1974.
    • (1974) C. R. Acad. Sci. Paris , vol.278 , pp. 957-960
    • Miellou, J.-C.1
  • 160
    • 0016487989 scopus 로고
    • Algorithmes de relaxation chaotique a retards
    • J.-C. Miellou, "Algorithmes de relaxation chaotique a retards." RAIRO R1:55-82, 1975.
    • (1975) RAIRO , vol.R1 , pp. 55-82
    • Miellou, J.-C.1
  • 162
    • 0038396136 scopus 로고    scopus 로고
    • Strong rank revealing lu factorizations
    • L. Miranian and M. Gu, "Strong rank revealing LU factorizations." Lin. Alg. Appl. 367:1-16, 2003.
    • (2003) Lin. Alg. Appl. , vol.367 , pp. 1-16
    • Miranian, L.1    Gu, M.2
  • 167
    • 0003254248 scopus 로고
    • Interior-point polynomial methods in convex programming
    • SIAM, Philadelphia
    • Y. Nesterov and A. Nemirovskii. Interior-Point Polynomial Methods in Convex Programming. Studies in Applied Mathematics 13. SIAM, Philadelphia, 1994.
    • (1994) Studies in Applied Mathematics , vol.13
    • Nesterov, Y.1    Nemirovskii, A.2
  • 171
    • 0000115216 scopus 로고
    • Robust regression computation using iteratively reweighted least squares
    • D. P. O'Leary, "Robust regression computation using iteratively reweighted least squares." SIAM J. Matrix. Anal. Appl. 22:466-480, 1990.
    • (1990) SIAM J. Matrix. Anal. Appl. , vol.22 , pp. 466-480
    • O'Leary, D.P.1
  • 172
    • 84876554932 scopus 로고    scopus 로고
    • Variable projection for nonlinear least squares problems
    • Submitted for publication
    • D. P. O'Leary and B. W. Rust, "Variable projection for nonlinear least squares problems." Submitted for publication in Computational Optimization and Applications (2011). Also at: http://www.cs.umd.edu/users/oleary/software/varpro.pdf.
    • (2011) Computational Optimization and Applications
    • O'Leary, D.P.1    Rust, B.W.2
  • 174
    • 0016556025 scopus 로고
    • Some special nonlinear least squares problems
    • M. R. Osborne, "Some special nonlinear least squares problems." SIAM J. Numer. Anal. 12:571-592, 1975.
    • (1975) SIAM J. Numer. Anal. , vol.12 , pp. 571-592
    • Osborne, M.R.1
  • 175
    • 0000085672 scopus 로고
    • A modified prony algorithm for fitting functions defined by difference equations
    • M. R. Osborne and G. K. Smyth, "A modified Prony algorithm for fitting functions defined by difference equations." SIAM J. Sci. Comp. 12:362-382, 1991.
    • (1991) SIAM J. Sci. Comp. , vol.12 , pp. 362-382
    • Osborne, M.R.1    Smyth, G.K.2
  • 176
    • 0000146564 scopus 로고
    • A modified prony algorithm for exponential function fitting
    • M. R. Osborne and G. K. Smyth, "A modified Prony algorithm for exponential function fitting." SIAM J. Sci. Comp. 16:119-138, 1995.
    • (1995) SIAM J. Sci. Comp. , vol.16 , pp. 119-138
    • Osborne, M.R.1    Smyth, G.K.2
  • 177
    • 54549121541 scopus 로고    scopus 로고
    • Separable least squares, variable projections, and the gauss-newton algorithm
    • M. R. Osborne, "Separable least squares, variable projections, and the Gauss-Newton algorithm." ETNA 28:1-15, 2007.
    • (2007) ETNA , vol.28 , pp. 1-15
    • Osborne, M.R.1
  • 178
    • 51249195842 scopus 로고
    • Determinanten mit ueberwiegender hauptdiagonale and die absolute konvergenz von linearen iterationsprozessen
    • A. Ostrowski, "Determinanten mit ueberwiegender Hauptdiagonale and die absolute Konvergenz von linearen Iterationsprozessen." Comm. Math. Helv. 30:175-210, 1955.
    • (1955) Comm. Math. Helv. , vol.30 , pp. 175-210
    • Ostrowski, A.1
  • 179
    • 0039943513 scopus 로고
    • LSQR: An algorithm for sparse linear equations and sparse least squares
    • C. C. Paige and M. A. Saunders, "LSQR: An algorithm for sparse linear equations and sparse least squares." ACM TOMS 8:43-71, 1982.
    • (1982) ACM TOMS , vol.8 , pp. 43-71
    • Paige, C.C.1    Saunders, M.A.2
  • 180
    • 33746132377 scopus 로고    scopus 로고
    • Core problems in linear algebraic systems
    • C. C. Paige and Z. Strakos, "Core problems in linear algebraic systems." SIAM J. Matrix Anal. Appl. 27:861-875, 2006.
    • (2006) SIAM J. Matrix Anal. Appl. , vol.27 , pp. 861-875
    • Paige, C.C.1    Strakos, Z.2
  • 181
    • 0000014434 scopus 로고    scopus 로고
    • A generalized learning paradigm exploiting the structure of feedforward neural networks
    • R. Parisi, E. D. Di Claudio, G. Orlandi and B. D. Rao, "A generalized learning paradigm exploiting the structure of feedforward neural networks." IEEE Transactions on Neural Networks 7:1450-1460, 1996.
    • (1996) IEEE Transactions on Neural Networks , vol.7 , pp. 1450-1460
    • Parisi, R.1    Di Claudio, E.D.2    Orlandi, G.3    Rao, B.D.4
  • 182
    • 0027151141 scopus 로고
    • Analysis and synthesis of feedforward neural networks using discrete affine wavelet transformations
    • Y. C. Pati and P. S. Krishnaprasad, "Analysis and synthesis of feedforward neural networks using discrete affine wavelet transformations." IEEE Trans. Neural Networks 4:73-85, 1993.
    • (1993) IEEE Trans. Neural Networks , vol.4 , pp. 73-85
    • Pati, Y.C.1    Krishnaprasad, P.S.2
  • 183
    • 0000622932 scopus 로고
    • Accelerating the convergence of discretization algorithms
    • V. Pereyra, "Accelerating the convergence of discretization algorithms." SIAM J. Numer. Anal. 4:508-533, 1967.
    • (1967) SIAM J. Numer. Anal. , vol.4 , pp. 508-533
    • Pereyra, V.1
  • 184
    • 0002303640 scopus 로고
    • Iterative methods for solving nonlinear least squares problems
    • V. Pereyra, "Iterative methods for solving nonlinear least squares problems." SIAM J. Numer. Anal. 4:27-36, 1967.
    • (1967) SIAM J. Numer. Anal. , vol.4 , pp. 27-36
    • Pereyra, V.1
  • 185
    • 34250516362 scopus 로고
    • Stability of general systems of linear equations
    • V. Pereyra, "Stability of general systems of linear equations." Aeq. Math. 2:194-206, 1969.
    • (1969) Aeq. Math. , vol.2 , pp. 194-206
    • Pereyra, V.1
  • 186
    • 84907761983 scopus 로고
    • Stabilizing linear least squares problems
    • V. Pereyra, "Stabilizing linear least squares problems." Proc. IFIP, Suppl. 68:119-121, 1969.
    • (1969) Proc. IFIP , pp. 119-121
    • Pereyra, V.1
  • 187
    • 0030428835 scopus 로고
    • Modeling, ray tracing, and block nonlinear travel-time inversion in 3D
    • V. Pereyra, "Modeling, ray tracing, and block nonlinear travel-time inversion in 3D." Pure and App. Geoph. 48:345-386, 1995.
    • (1995) Pure and App. Geoph. , vol.48 , pp. 345-386
    • Pereyra, V.1
  • 188
    • 0033541910 scopus 로고    scopus 로고
    • Asynchronous distributed solution of large scale nonlinear inversion problems
    • V. Pereyra, "Asynchronous distributed solution of large scale nonlinear inversion problems." J. App. Numer. Math. 30:31-40, 1999.
    • (1999) J. App. Numer. Math. , vol.30 , pp. 31-40
    • Pereyra, V.1
  • 190
    • 59349086143 scopus 로고    scopus 로고
    • Fast computation of equispaced pareto manifolds and pareto fronts for multiobjective optimization problems
    • V. Pereyra, "Fast computation of equispaced Pareto manifolds and Pareto fronts for multiobjective optimization problems." Math. Comp. in Simulation 79:1935-1947, 2009.
    • (2009) Math. Comp. in Simulation , vol.79 , pp. 1935-1947
    • Pereyra, V.1
  • 191
    • 5244350794 scopus 로고
    • Asynchronous global optimization techniques for medium and large inversion problems
    • V. Pereyra, M. Koshy and J. Meza, "Asynchronous global optimization techniques for medium and large inversion problems." SEG Annual Meeting Extended Abstracts 65:1091-1094, 1995.
    • (1995) SEG Annual Meeting Extended Abstracts , vol.65 , pp. 1091-1094
    • Pereyra, V.1    Koshy, M.2    Meza, J.3
  • 192
    • 21644469958 scopus 로고    scopus 로고
    • Application of optimization techniques to finite element analysis of piezocomposite devices
    • Montreal, CANADA
    • V. Pereyra and P. Reynolds, "Application of optimization techniques to finite element analysis of piezocomposite devices." IEEE Ultrasonics Symposium, Montreal, CANADA, 2004.
    • (2004) IEEE Ultrasonics Symposium
    • Pereyra, V.1    Reynolds, P.2
  • 193
    • 84936285151 scopus 로고
    • Computation of the pseudoinverse of a matrix of unknown rank
    • Computer Science Department, Stanford University, Stanford, CA
    • V. Pereyra and J. B. Rosen, Computation of the Pseudoinverse of a Matrix of Unknown Rank. Report CS 13, 39 pp. Computer Science Department, Stanford University, Stanford, CA, 1964.
    • (1964) Report CS
    • Pereyra, V.1    Rosen, J.B.2
  • 194
    • 84865480112 scopus 로고    scopus 로고
    • Equispaced pareto front construction for constrained biobjective optimization
    • Stanford, CA, Also CSRCR2009- 05, San Diego State University, 2009. In Press, Mathematical and Computer Modelling, 2012
    • V. Pereyra, M. Saunders and J. Castillo, Equispaced Pareto Front Construction for Constrained Biobjective Optimization. SOL Report- 2010-1, Stanford University, Stanford, CA, 2010. Also CSRCR2009- 05, San Diego State University, 2009. In Press, Mathematical and Computer Modelling, 2012.
    • (2010) SOL Report, Stanford University
    • Pereyra, V.1    Saunders, M.2    Castillo, J.3
  • 195
    • 84966225977 scopus 로고
    • Efficient computer manipulation of tensor products with applications in multidimensional approximation
    • V. Pereyra and G. Scherer, "Efficient computer manipulation of tensor products with applications in multidimensional approximation." Math. Comp. 27:595-605, 1973.
    • (1973) Math. Comp. , vol.27 , pp. 595-605
    • Pereyra, V.1    Scherer, G.2
  • 196
    • 0036132798 scopus 로고    scopus 로고
    • Least squares scattered data fitting by truncated SVD
    • V. Pereyra and G. Scherer, "Least squares scattered data fitting by truncated SVD." Applied Numer. Math. 40:73-86, 2002.
    • (2002) Applied Numer. Math. , vol.40 , pp. 73-86
    • Pereyra, V.1    Scherer, G.2
  • 197
    • 0037215279 scopus 로고    scopus 로고
    • Large scale least squares data fitting
    • V. Pereyra and G. Scherer, "Large scale least squares data fitting." Applied Numer. Math. 44:225-239, 2002.
    • (2002) Applied Numer. Math. , vol.44 , pp. 225-239
    • Pereyra, V.1    Scherer, G.2
  • 198
    • 84879377331 scopus 로고    scopus 로고
    • Exponential data fitting
    • Ed. V. Pereyra and G. Scherer. Bentham Books, Oak Park, IL
    • V. Pereyra and G. Scherer, "Exponential data fitting." In Exponential Data Fitting and Its Applications, Ed. V. Pereyra and G. Scherer. Bentham Books, Oak Park, IL, 2010.
    • (2010) Exponential Data Fitting and its Applications
    • Pereyra, V.1    Scherer, G.2
  • 201
    • 0014827294 scopus 로고
    • The least squares problem and pseudo-inverses
    • G. Peters and J. H. Wilkinson, "The least squares problem and pseudo-inverses." The Computer Journal 13:309-316, 1969.
    • (1969) The Computer Journal , vol.13 , pp. 309-316
    • Peters, G.1    Wilkinson, J.H.2
  • 203
    • 0004042460 scopus 로고
    • Proben 1 - A set of benchmark neural network problems and benchmarking rules
    • Universitaet Karlsruhe
    • L. Prechelt, Proben 1-A Set of Benchmark Neural Network Problems and Benchmarking Rules. Technical Report 21, Fakultaet fuer Informatik, Universitaet Karlsruhe, 1994.
    • (1994) Technical Report, Fakultaet Fuer Informatik
    • Prechelt, L.1
  • 204
    • 0001799628 scopus 로고
    • Essai experimental et analytique: Sur les lois de la dilatabilite de fluides elastique et sur celles de la force expansive de la vapeur de l'alkool, a differentes temperatures
    • Baron Gaspard Riche de Prony, "Essai experimental et analytique: Sur les lois de la dilatabilite de fluides elastique et sur celles de la force expansive de la vapeur de l'alkool, a differentes temperatures." J. Ecole Polyt. 1:24-76, 1795.
    • (1795) J. Ecole Polyt. , vol.1 , pp. 24-76
    • De Prony, B.G.R.1
  • 206
    • 0000509093 scopus 로고
    • Fast qr decomposition of vandermonde-like matrices and polynomial least squares approximations
    • L. Reichel, "Fast QR decomposition of Vandermonde-like matrices and polynomial least squares approximations." SIAM J. Matrix Anal. Appl. 12:552-564, 1991.
    • (1991) SIAM J. Matrix Anal. Appl. , vol.12 , pp. 552-564
    • Reichel, L.1
  • 207
    • 17444432191 scopus 로고    scopus 로고
    • Efficient algorithms for solution of regularized total least squares
    • R. A. Renaut and H. Guo, "Efficient algorithms for solution of regularized total least squares." SIAM J. Matrix Anal. Appl. 26:457-476, 2005.
    • (2005) SIAM J. Matrix Anal. Appl. , vol.26 , pp. 457-476
    • Renaut, R.A.1    Guo, H.2
  • 208
    • 84968520223 scopus 로고
    • Experiments on gram-schmidt orthogonalization
    • J. R. Rice, "Experiments on Gram-Schmidt orthogonalization." Math. Comp. 20:325-328, 1966.
    • (1966) Math. Comp. , vol.20 , pp. 325-328
    • Rice, J.R.1
  • 209
    • 0042855805 scopus 로고
    • Minimum and basic solutions to singular systems
    • J. B. Rosen, "Minimum and basic solutions to singular systems." J. SIAM 12:156-162, 1964.
    • (1964) J. SIAM , vol.12 , pp. 156-162
    • Rosen, J.B.1
  • 210
    • 11744359666 scopus 로고
    • A gradient projection algorithm for nonlinear constraints
    • Ed. F. A. Lootsma, Academic Press, New York
    • J. B. Rosen and J. Kreuser, "A gradient projection algorithm for nonlinear constraints." In Numerical Methods for Non-Linear Optimization. Ed. F. A. Lootsma, Academic Press, New York, pp. 297-300, 1972.
    • (1972) Numerical Methods for Non-Linear Optimization , pp. 297-300
    • Rosen, J.B.1    Kreuser, J.2
  • 211
    • 84918609611 scopus 로고
    • A case study on programming for parallel processors
    • Yorktown Heights, New York
    • J. Rosenfeld, A Case Study on Programming for Parallel Processors. Research Report RC-1864, IBM Watson Research Center, Yorktown Heights, New York, 1967.
    • (1967) Research Report, IBM Watson Research Center
    • Rosenfeld, J.1
  • 212
    • 0002832234 scopus 로고
    • Algorithms for separable non-linear least squares problems
    • Å. Ruhe and P-Å. Wedin, "Algorithms for separable non-linear least squares problems." SIAM Rev. 22:318-337, 1980.
    • (1980) SIAM Rev. , vol.22 , pp. 318-337
    • Ruhe Å.1    Wedin P.-Å.2
  • 214
    • 84957736798 scopus 로고    scopus 로고
    • B. W. Rust, http://math.nist.gov/BRust/Gallery.html, 2011.
    • (2011)
    • Rust, B.W.1
  • 215
    • 0003640987 scopus 로고    scopus 로고
    • Truncating the singular value decomposition for ill- posed problems
    • National Institute of Standards and Technology
    • B. W. Rust, Truncating the Singular Value Decomposition for Ill- Posed Problems. Tech. Report NISTIR 6131, Mathematics and Computer Sciences Division, National Institute of Standards and Technology, 1998.
    • (1998) Tech. Report NISTIR, Mathematics and Computer Sciences Division
    • Rust, B.W.1
  • 216
    • 44449162474 scopus 로고    scopus 로고
    • Residual periodograms for choosing regularization parameters for ill-posed problems
    • B. W. Rust and D. P. O'Leary, "Residual periodograms for choosing regularization parameters for ill-posed problems." Inverse Problems 24, 2008.
    • (2008) Inverse Problems , vol.24
    • Rust, B.W.1    O'Leary, D.P.2
  • 218
    • 0029736203 scopus 로고    scopus 로고
    • Finite termination of asynchronous iterative algorithms
    • S. A. Savari and D. P. Bertsekas, "Finite termination of asynchronous iterative algorithms." Parallel Comp. 22:39-56, 1996.
    • (1996) Parallel Comp. , vol.22 , pp. 39-56
    • Savari, S.A.1    Bertsekas, D.P.2
  • 219
    • 0000485257 scopus 로고
    • Fast lp solution of large, sparse, linear systems: Application to seismic travel time tomography
    • J. A. Scales, A. Gersztenkorn and S. Treitel, "Fast lp solution of large, sparse, linear systems: Application to seismic travel time tomography." J. Comp. Physics 75:314-333, 1988.
    • (1988) J. Comp. Physics , vol.75 , pp. 314-333
    • Scales, J.A.1    Gersztenkorn, A.2    Treitel, S.3
  • 221
    • 84980078021 scopus 로고
    • Relaxation methods for linear equations
    • S. Schechter, "Relaxation methods for linear equations." Comm. Pure Appl. Math. 12:313-335, 1959.
    • (1959) Comm. Pure Appl. Math. , vol.12 , pp. 313-335
    • Schechter, S.1
  • 222
    • 0028182144 scopus 로고
    • An oscillation in the global climate system of period 65-70 years
    • M. E. Schlesinger and N. Ramankutty, "An oscillation in the global climate system of period 65-70 years." Nature 367:723-726, 1994.
    • (1994) Nature , vol.367 , pp. 723-726
    • Schlesinger, M.E.1    Ramankutty, N.2
  • 224
    • 0003800250 scopus 로고
    • Cambridge University Press, second edition, Cambridge
    • R. Sheriff and L. Geldart, Exploration Seismology. Cambridge University Press, second edition, Cambridge, 1995.
    • (1995) Exploration Seismology
    • Sheriff, R.1    Geldart, L.2
  • 225
    • 18244394807 scopus 로고    scopus 로고
    • Regularized total least squares based on quadratic eigenvalue problem solvers
    • D. Sima, S. Van Huffel and G. Golub, "Regularized total least squares based on quadratic eigenvalue problem solvers." BIT 44:793-812, 2004.
    • (2004) BIT , vol.44 , pp. 793-812
    • Sima, D.1    Van Huffel, S.2    Golub, G.3
  • 226
    • 84957745526 scopus 로고    scopus 로고
    • Spline2. http://www.structureandchange.3me.tudelft.nl/.
    • Spline2
  • 227
    • 0031380999 scopus 로고    scopus 로고
    • Separable non-linear least squares minimization-possible improvements for neural net fitting
    • Amelia Island Plantation, FL
    • J. Sjöberg and M. Viberg, "Separable non-linear least squares minimization-possible improvements for neural net fitting." IEEE Workshop in Neural Networks for Signal Processing, Amelia Island Plantation, FL, 1997.
    • (1997) IEEE Workshop in Neural Networks for Signal Processing
    • Sjöberg, J.1    Viberg, M.2
  • 228
    • 84882580713 scopus 로고    scopus 로고
    • Accurate calculations of the high-frequency impedance matrix for vlsi interconnects and inductors above a multi-layer substrate: A VARPRO success story
    • Eds. V. Pereyra and G. Scherer. Bentham Books, Oak Park, IL
    • N. Srivastava, R. Suaya, V. Pereyra and K. Banerjee, "Accurate calculations of the high-frequency impedance matrix for VLSI interconnects and inductors above a multi-layer substrate: A VARPRO success story." In Exponential Data Fitting and Its Applications, Eds. V. Pereyra and G. Scherer. Bentham Books, Oak Park, IL, 2010.
    • (2010) Exponential Data Fitting and its Applications
    • Srivastava, N.1    Suaya, R.2    Pereyra, V.3    Banerjee, K.4
  • 231
    • 0001918839 scopus 로고
    • On the invariance of perturbed null vectors under column scaling
    • G. W. Stewart, "On the invariance of perturbed null vectors under column scaling." Numer. Math. 44:61-65, 1984.
    • (1984) Numer. Math. , vol.44 , pp. 61-65
    • Stewart, G.W.1
  • 232
    • 0004094905 scopus 로고    scopus 로고
    • Basic Decompositions. SIAM, Philadelphia
    • G. W. Stewart, Matrix Algorithms. Volume I: Basic Decompositions. SIAM, Philadelphia, 1998.
    • (1998) Matrix Algorithms , vol.1
    • Stewart, G.W.1
  • 234
    • 38149042129 scopus 로고    scopus 로고
    • Freestyle data fitting and global temperatures
    • B. J. Thijsse and B. Rust, "Freestyle data fitting and global temperatures." Computing in Sci. and Eng. pp. 49-59, 2008.
    • (2008) Computing in Sci. and Eng. , pp. 49-59
    • Thijsse, B.J.1    Rust, B.2
  • 235
    • 85194972808 scopus 로고    scopus 로고
    • Regression shrinkage and selection via the lasso
    • Series B (Methodological)
    • R. Tibshirani, "Regression shrinkage and selection via the lasso." Journal of the Royal Statistical Society. Series B (Methodological) 58:267-288, 1996.
    • (1996) Journal of the Royal Statistical Society , vol.58 , pp. 267-288
    • Tibshirani, R.1
  • 236
    • 0000418073 scopus 로고
    • On the stability of inverse problems
    • A. N. Tikhonov, "On the stability of inverse problems." Dokl. Akad. Nauk SSSR 39:195-198, 1943.
    • (1943) Dokl. Akad. Nauk SSSR , vol.39 , pp. 195-198
    • Tikhonov, A.N.1
  • 240
    • 65649137930 scopus 로고    scopus 로고
    • Probing the pareto frontier for basis pursuit solutions
    • E. van den Berg and M. P. Friedlander, "Probing the Pareto frontier for basis pursuit solutions." SIAM J. Sci. Comp. 31:890-912, 2008.
    • (2008) SIAM J. Sci. Comp. , vol.31 , pp. 890-912
    • Van Den Berg, E.1    Friedlander, M.P.2
  • 241
    • 84856046625 scopus 로고    scopus 로고
    • Sparse optimization with least-squares constraints
    • E. van den Berg and M. P. Friedlander, "Sparse optimization with least-squares constraints." SIAM J. Optim. 21:1201-1229, 2011.
    • (2011) SIAM J. Optim. , vol.21 , pp. 1201-1229
    • Van Den Berg, E.1    Friedlander, M.P.2
  • 243
    • 0002090018 scopus 로고
    • Condition numbers and equilibration of matrices
    • A. van der Sluis, "Condition numbers and equilibration of matrices." Numer. Math. 14:14-23, 1969.
    • (1969) Numer. Math. , vol.14 , pp. 14-23
    • Van Der Sluis, A.1
  • 244
    • 0023860494 scopus 로고
    • Accurate quantification of in vivo 31p nmr signals using the variable projection method and prior knowledge
    • J. W. van der Veen, R. de Beer, P. R. Luyten and D. Van Ormondt, "Accurate quantification of in vivo 31P NMR signals using the variable projection method and prior knowledge." Magn. Reson. Med. 6:92- 98, 1988.
    • (1988) Magn. Reson. Med. , vol.6 , pp. 92-98
    • Van Der Veen, J.W.1    De Beer, R.2    Luyten, P.R.3    Van Ormondt, D.4
  • 245
    • 0346308381 scopus 로고    scopus 로고
    • Improved method for accurate and efficient quantification of MRS data with use of prior knowledge
    • L. Vanhamme, A. van den Boogaart and S. Van Huffel, "Improved method for accurate and efficient quantification of MRS data with use of prior knowledge." J. Magn. Reson. 129:35-43, 1997.
    • (1997) J. Magn. Reson. , vol.129 , pp. 35-43
    • Vanhamme, L.1    Van Den Boogaart, A.2    Van Huffel, S.3
  • 246
    • 0033185631 scopus 로고    scopus 로고
    • Time-domain quantification of series of biomedical magnetic resonance spectroscopy signals
    • L. Vanhamme, S. Van Huffel, P. Van Hecke and D. van Ormondt, "Time-domain quantification of series of biomedical magnetic resonance spectroscopy signals." J. Magn. Reson. 140:120-130, 1999.
    • (1999) J. Magn. Reson. , vol.140 , pp. 120-130
    • Vanhamme, L.1    Van Huffel, S.2    Van Hecke, P.3    Van Ormondt, D.4
  • 247
    • 0034146105 scopus 로고    scopus 로고
    • Frequency-selective quantification of biomedical magnetic resonance spectroscopy data
    • L. Vanhamme, T. Sundin, P. Van Hecke, S. Van Huffel and R. Pintelon, "Frequency-selective quantification of biomedical magnetic resonance spectroscopy data." J. Magn. Reson. 143:1-16, 2000.
    • (2000) J. Magn. Reson. , vol.143 , pp. 1-16
    • Vanhamme, L.1    Sundin, T.2    Van Hecke, P.3    Van Huffel, S.4    Pintelon, R.5
  • 248
    • 38249018339 scopus 로고
    • Partial singular value decomposition algorithm
    • S. Van Huffel, 'Partial singular value decomposition algorithm." J. Comp. Appl. Math. 33:105-112, 1990.
    • (1990) J. Comp. Appl. Math. , vol.33 , pp. 105-112
    • Van Huffel, S.1
  • 249
    • 84985406595 scopus 로고    scopus 로고
    • Optimal backward perturbation bounds for the linear least squares problem
    • B. Walden, R. Karlsson and J.-G. Sun, "Optimal backward perturbation bounds for the linear least squares problem." Numer. Linear Algebra Appl. 2:271-286, 2005.
    • (2005) Numer. Linear Algebra Appl. , vol.2 , pp. 271-286
    • Walden, B.1    Karlsson, R.2    Sun, J.-G.3
  • 250
    • 26444503697 scopus 로고    scopus 로고
    • Nearest neighbors in least squares data imputation algorithms with different missing patterns
    • I. Wasito and B. Mirkin, "Nearest neighbors in least squares data imputation algorithms with different missing patterns." Comp. Stat. & Data Analysis 50: 926-949, 2006.
    • (2006) Comp. Stat. & Data Analysis , vol.50 , pp. 926-949
    • Wasito, I.1    Mirkin, B.2
  • 253
    • 0012927086 scopus 로고
    • Application of projection learning to the detection of urban areas in SPOT satellite images
    • Sophia-Antipolis, France
    • K. Weigl, G. Giraudon and M. Berthod, Application of Projection Learning to the Detection of Urban Areas in SPOT Satellite Images. Report #2143, INRIA, Programe Robotique, Image et Vision, Sophia-Antipolis, France, 1993.
    • (1993) Report, INRIA, Programe Robotique, Image et Vision
    • Weigl, K.1    Giraudon, G.2    Berthod, M.3
  • 255
    • 0003494064 scopus 로고
    • Prentice- Hall, Englewood Cliffs, NJ, Reprint Dover, New York, 1994
    • J. H. Wilkinson, Rounding Errors in Algebraic Processes. Prentice- Hall, Englewood Cliffs, NJ, 1963. Reprint Dover, New York, 1994.
    • (1963) Rounding Errors in Algebraic Processes
    • Wilkinson, J.H.1
  • 256
    • 0012982836 scopus 로고
    • Nonlinear iterative partial least squares (nipals) estimation procedures
    • H. Wold and E. Lyttkens, "Nonlinear iterative partial least squares (NIPALS) estimation procedures." Bull. ISI 43:29-51, 1969.
    • (1969) Bull. ISI , vol.43 , pp. 29-51
    • Wold, H.1    Lyttkens, E.2
  • 257
    • 0001681052 scopus 로고
    • The collinearity problem in linear regression. The partial least squares (pls) approach to generalized inverses
    • S. Wold, A. Ruhe, H. Wold and W. J. Dunn, "The collinearity problem in linear regression. The partial least squares (PLS) approach to generalized inverses." SIAM J. Sci. Stat. Comput. 5:735-743, 1984.
    • (1984) SIAM J. Sci. Stat. Comput. , vol.5 , pp. 735-743
    • Wold, S.1    Ruhe, A.2    Wold, H.3    Dunn, W.J.4
  • 258
    • 0001472922 scopus 로고
    • Iteratively reweighted least squares: Algorithms, convergence analysis, and numerical comparisons
    • R. Wolke and H. Schwetlick, "Iteratively reweighted least squares: Algorithms, convergence analysis, and numerical comparisons." SIAM J. Sci. Stat. Comput. 9:907-921, 1988.
    • (1988) SIAM J. Sci. Stat. Comput. , vol.9 , pp. 907-921
    • Wolke, R.1    Schwetlick, H.2
  • 260
    • 0001421395 scopus 로고
    • Algorithms for non-linear least squares with linear inequality constraints
    • S. J. Wright, J. N. Holt, "Algorithms for non-linear least squares with linear inequality constraints." SIAM J. Sci. and Stat. Comput. 6:1033-1048, 1985.
    • (1985) SIAM J. Sci. and Stat. Comput , vol.6 , pp. 1033-1048
    • Wright, S.J.1    Holt, J.N.2
  • 261
    • 27844519698 scopus 로고
    • On the convergence and precision of a process of successive differential corrections
    • P. Zadunaisky and V. Pereyra, "On the convergence and precision of a process of successive differential corrections." Proc. IFIPS 65, 1965.
    • (1965) Proc. IFIPS , vol.65
    • Zadunaisky, P.1    Pereyra, V.2
  • 262
    • 0009923933 scopus 로고    scopus 로고
    • Singular values of a classical matrix
    • H. Zha, "Singular values of a classical matrix." The American Mathematical Monthly 104:172-173, 1997.
    • (1997) The American Mathematical Monthly , vol.104 , pp. 172-173
    • Zha, H.1
  • 264
    • 84957740614 scopus 로고    scopus 로고
    • NEOS Wiki. http://www.neos-guide.org.
    • NEOS Wiki


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.