메뉴 건너뛰기




Volumn 26, Issue 6, 2005, Pages 2133-2159

Algorithms for numerical analysis in high dimensions

Author keywords

Algorithms in high dimensions; Alternating least squares; Curse of dimensionality; Multidimensional function; Multidimensional operator; Separated representation; Separated solutions of linear systems; Separation of variables; Separation rank reduction

Indexed keywords

COMPUTATIONAL COMPLEXITY; FUNCTION EVALUATION; LINEAR SYSTEMS; NUMERICAL ANALYSIS; PROBLEM SOLVING; WAVE EQUATIONS;

EID: 27844496824     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/040604959     Document Type: Article
Times cited : (320)

References (46)
  • 2
    • 0003019969 scopus 로고    scopus 로고
    • Fast spectral projection algorithms for density-matrix computations
    • G. BEYLKIN, N. COULT, AND M. J. MOHLENKAMP, Fast spectral projection algorithms for density-matrix computations, J. Comput. Phys., 152 (1999), pp. 32-54.
    • (1999) J. Comput. Phys. , vol.152 , pp. 32-54
    • Beylkin, G.1    Coult, N.2    Mohlenkamp, M.J.3
  • 3
    • 0036679114 scopus 로고    scopus 로고
    • Numerical operator calculus in higher dimensions
    • G. BEYLKIN AND M. J. MOHLENKAMP, Numerical operator calculus in higher dimensions, Proc. Natl. Acad. Sci. USA, 99 (2002), pp. 10246-10251.
    • (2002) Proc. Natl. Acad. Sci. USA , vol.99 , pp. 10246-10251
    • Beylkin, G.1    Mohlenkamp, M.J.2
  • 4
    • 3943060186 scopus 로고    scopus 로고
    • On generalized Gaussian quadratures for exponentials and their applications
    • G. BEYLKIN AND L. MONZÓN, On generalized Gaussian quadratures for exponentials and their applications, Appl. Comput. Harmon. Anal., 12 (2002), pp. 332-373.
    • (2002) Appl. Comput. Harmon. Anal. , vol.12 , pp. 332-373
    • Beylkin, G.1    Monzón, L.2
  • 6
    • 13444255982 scopus 로고    scopus 로고
    • Wave propagation using bases for bandlimited functions
    • G. BEYLKIN AND K. SANDBERG, Wave propagation using bases for bandlimited functions, Wave Motion, 41 (2005), pp. 263-291.
    • (2005) Wave Motion , vol.41 , pp. 263-291
    • Beylkin, G.1    Sandberg, K.2
  • 7
    • 27844518677 scopus 로고    scopus 로고
    • A short proof of an identity of Sylvester
    • G. BHATNAGAR, A short proof of an identity of Sylvester, Int. J. Math. Math. Sci., 22 (1999), pp. 431-435.
    • (1999) Int. J. Math. Math. Sci. , vol.22 , pp. 431-435
    • Bhatnagar, G.1
  • 8
    • 0030813663 scopus 로고    scopus 로고
    • Parafac. tutorial & applications
    • R. BRO, Parafac. tutorial & applications, Chemom. Intell. Lab. Syst., 38 (1997), pp. 149-171.
    • (1997) Chemom. Intell. Lab. Syst. , vol.38 , pp. 149-171
    • Bro, R.1
  • 10
    • 27844477618 scopus 로고    scopus 로고
    • Remarkable matrices and trigonometric identities. II
    • F. CALOGERO, Remarkable matrices and trigonometric identities. II, Commun. Appl. Anal., 3 (1999), pp. 267-270.
    • (1999) Commun. Appl. Anal. , vol.3 , pp. 267-270
    • Calogero, F.1
  • 11
    • 0003324526 scopus 로고    scopus 로고
    • Classical Many-Body Problems Amenable to Exact Treatments
    • Springer, Berlin
    • F. CALOGERO, Classical Many-Body Problems Amenable to Exact Treatments, Lecture Notes in Phys., 66, Springer, Berlin, 2001.
    • (2001) Lecture Notes in Phys. , vol.66
    • Calogero, F.1
  • 12
    • 0032612381 scopus 로고    scopus 로고
    • Higher-order contrasts for independent component analysis
    • J.-F. CARDOSO, Higher-order contrasts for independent component analysis, Neural Comp., 11 (1999), pp. 157-192.
    • (1999) Neural Comp. , vol.11 , pp. 157-192
    • Cardoso, J.-F.1
  • 13
    • 0027812550 scopus 로고
    • Blind beamforming for non-Gaussian signals
    • J.-F. CARDOSO AND A. SOULOUMIAC, Blind beamforming for non-Gaussian signals, IEE Proceedings F, 140 (1993), pp. 362-370.
    • (1993) IEE Proceedings F , vol.140 , pp. 362-370
    • Cardoso, J.-F.1    Souloumiac, A.2
  • 16
    • 2942606241 scopus 로고    scopus 로고
    • Combining kronecker product approximation with discrete wavelet transforms to solve dense, function-related linear systems
    • J. M. FORD AND E. E. TYRTYSHNIKOV, Combining Kronecker product approximation with discrete wavelet transforms to solve dense, function-related linear systems, SIAM J. Sci. Comput., 25 (2003), pp. 961-981.
    • (2003) SIAM J. Sci. Comput. , vol.25 , pp. 961-981
    • Ford, J.M.1    Tyrtyshnikov, E.E.2
  • 19
    • 35248847018 scopus 로고    scopus 로고
    • Multiresolution quantum chemistry in multiwavelet bases
    • Computational Science - ICCS 2003, P. M. A. Sloot et al., eds., Springer, Berlin
    • R. HARRISON, G. FANN, T. YANAI, AND G. BEYLKIN, Multiresolution quantum chemistry in multiwavelet bases, in Computational Science - ICCS 2003, P. M. A. Sloot et al., eds., Lecture Notes in Comput. Sci. 2660, Springer, Berlin, 2003, pp. 103-110.
    • (2003) Lecture Notes in Comput. Sci. 2660 , pp. 103-110
    • Harrison, R.1    Fann, G.2    Yanai, T.3    Beylkin, G.4
  • 20
    • 11044224123 scopus 로고    scopus 로고
    • Multiresolution quantum chemistry: Basic theory and initial applications
    • R. HARRISON, G. FANN, T. YANAI, Z. GAN, AND G. BEYLKIN, Multiresolution quantum chemistry: Basic theory and initial applications, J. Chem. Phys., 121 (2004), pp. 11587-11598.
    • (2004) J. Chem. Phys. , vol.121 , pp. 11587-11598
    • Harrison, R.1    Fann, G.2    Yanai, T.3    Gan, Z.4    Beylkin, G.5
  • 21
    • 0002740437 scopus 로고
    • Foundations of the PARAFAC procedure: Model and conditions for an "explanatory" multimodal factor analysis
    • UCLA
    • R. A. HARSHMAN, Foundations of the PARAFAC procedure: Model and Conditions for an "Explanatory" Multimodal Factor Analysis, Working Papers in Phonetics 16, UCLA, 1970, 1-84; also available online from http://publish.uwo.ca/~harshman/wpppfac0.pdf.
    • (1970) Working Papers in Phonetics 16 , pp. 1-84
    • Harshman, R.A.1
  • 22
    • 0032203448 scopus 로고    scopus 로고
    • An improved fast multipole, algorithm for potential fields
    • T. HRYCAK AND V. ROKHLIN, An improved fast multipole, algorithm for potential fields, SIAM J. Sci. Comput., 19 (1998), pp. 1804-1826.
    • (1998) SIAM J. Sci. Comput. , vol.19 , pp. 1804-1826
    • Hrycak, T.1    Rokhlin, V.2
  • 24
    • 0031572113 scopus 로고    scopus 로고
    • A fast spherical filter with uniform resolution
    • R. JAKOB-CHIEN AND B. K. ALPERT, A fast spherical filter with uniform resolution, J. Comput. Phys., 136 (1997), pp. 580-584.
    • (1997) J. Comput. Phys. , vol.136 , pp. 580-584
    • Jakob-Chien, R.1    Alpert, B.K.2
  • 25
    • 28144446316 scopus 로고
    • A fast direct algorithm for the solution of the Laplace equation on regions with fractal boundaries
    • P. JONES, J. MA, AND V. ROKHLIN, A fast direct algorithm for the solution of the Laplace equation on regions with fractal boundaries, J. Comput. Phys., 113 (1994), pp. 35-51.
    • (1994) J. Comput. Phys. , vol.113 , pp. 35-51
    • Jones, P.1    Ma, J.2    Rokhlin, V.3
  • 26
    • 36149019811 scopus 로고
    • Monte Carlo calculations of the ground state of three- And four-body nuclei
    • M. H. KALOS, Monte Carlo calculations of the ground state of three- and four-body nuclei, Phys. Rev. (2), 128 (1962), pp. 1791-1795.
    • (1962) Phys. Rev. , vol.128 , Issue.2 , pp. 1791-1795
    • Kalos, M.H.1
  • 27
    • 0036055687 scopus 로고    scopus 로고
    • Orthogonal tensor decompositions
    • T. G. KOLDA, Orthogonal tensor decompositions, SIAM J. Matrix Anal. Appl., 23 (2001), pp. 243-255.
    • (2001) SIAM J. Matrix Anal. Appl. , vol.23 , pp. 243-255
    • Kolda, T.G.1
  • 28
    • 0002332422 scopus 로고
    • Principal component analysis of three-mode data by means of alternating least squares algorithms
    • P. M. KROONENBERG AND J. DE LEEUW, Principal component analysis of three-mode data by means of alternating least squares algorithms, Psychometrika, 45 (1980), pp. 69-97.
    • (1980) Psychometrika , vol.45 , pp. 69-97
    • Kroonenberg, P.M.1    De Leeuw, J.2
  • 30
    • 0038207573 scopus 로고    scopus 로고
    • On the systematic improvement of fixed-node diffusion quantum Monte Carlo energies using natural orbital CI guide functions
    • A. LÜCHOW AND R. FINK, On the systematic improvement of fixed-node diffusion quantum Monte Carlo energies using natural orbital CI guide functions, J. Chem. Phys., 113 (2000), pp. 8457-8463.
    • (2000) J. Chem. Phys. , vol.113 , pp. 8457-8463
    • Lüchow, A.1    Fink, R.2
  • 31
    • 0002128340 scopus 로고
    • A q-analog of the Gauss summation theorem for hypergeometric series in U(n)
    • S. C. MILNE, A q-analog of the Gauss summation theorem for hypergeometric series in U(n), Adv. in Math., 72 (1988), pp. 59-131.
    • (1988) Adv. in Math. , vol.72 , pp. 59-131
    • Milne, S.C.1
  • 33
    • 0001241557 scopus 로고    scopus 로고
    • Canonical purification of the density matrix in electronic-structure theory
    • A. H. R. FALSER AND D. E. MANOLOPOULOS, Canonical purification of the density matrix in electronic-structure theory, Phys. Rev. B, 58 (1998), pp. 12704-12711.
    • (1998) Phys. Rev. B , vol.58 , pp. 12704-12711
    • Falser, A.H.R.1    Manolopoulos, D.E.2
  • 35
    • 84966225977 scopus 로고
    • Efficient computer manipulation of tensor products with applications to multidimensional approximation
    • V. PEREYRA AND G. SCHERER, Efficient computer manipulation of tensor products with applications to multidimensional approximation, Math. Comp., 27 (1973), pp. 595-605.
    • (1973) Math. Comp. , vol.27 , pp. 595-605
    • Pereyra, V.1    Scherer, G.2
  • 36
    • 0003634764 scopus 로고
    • Finite sums decompositions in mathematical analysis
    • John Wiley & Sons Ltd., Chichester, UK
    • T. M. RASSIAS AND J. ŠIMŠA, Finite Sums Decompositions in Mathematical Analysis, Pure Appl. Math. (N.Y.), John Wiley & Sons Ltd., Chichester, UK, 1995.
    • (1995) Pure Appl. Math. (N.Y.)
    • Rassias, T.M.1    Šimša, J.2
  • 38
    • 84979324358 scopus 로고
    • Iterative berechnung der reziproken matrix
    • G. SCHULZ, Iterative Berechnung der reziproken Matrix, Z. Angew. Math. Mech., 13 (1933), pp. 57-59.
    • (1933) Z. Angew. Math. Mech. , vol.13 , pp. 57-59
    • Schulz, G.1
  • 39
    • 77956755263 scopus 로고    scopus 로고
    • The configuration interaction method: Advances in highly correlated approaches
    • C. D. SHERRILL AND H. F. SCHAEFER III, The configuration interaction method: Advances in highly correlated approaches, Adv. in Quantum Chem., 127 (1999), pp. 143-269.
    • (1999) Adv. in Quantum Chem. , vol.127 , pp. 143-269
    • Sherrill, C.D.1    Schaefer III, H.F.2
  • 41
    • 0001861898 scopus 로고
    • Estimates of best bilinear approximations of periodic functions
    • V. N. TEMLYAKOV, Estimates of best bilinear approximations of periodic functions, Proc. Steklov Inst. Math., (1989), pp. 275-293.
    • (1989) Proc. Steklov Inst. Math. , pp. 275-293
    • Temlyakov, V.N.1
  • 42
    • 0742320626 scopus 로고    scopus 로고
    • Kronecker-product approximations for some function-related matrices
    • E. TYRTYSHNIKOV, Kronecker-product approximations for some function-related matrices, Linear Algebra Appl., 379 (2004), pp. 423-437.
    • (2004) Linear Algebra Appl. , vol.379 , pp. 423-437
    • Tyrtyshnikov, E.1
  • 43
    • 17144425622 scopus 로고    scopus 로고
    • Tensor approximations of matrices generated by asymptotically smooth functions
    • E. E. TYRTYSHNIKOV, Tensor approximations of matrices generated by asymptotically smooth functions, Mat. Sb., 194 (2003), pp. 147-160.
    • (2003) Mat. Sb. , vol.194 , pp. 147-160
    • Tyrtyshnikov, E.E.1
  • 44
    • 0002203498 scopus 로고
    • Approximation with Kronecker products
    • Proceedings of the Linear Algebra for Large Scale and Real-Time Applications (Leuven, 1992), Kluwer, Dordrecht, the Netherlands
    • C. F. VAN LOAN AND N. PITSIANIS, Approximation with Kronecker products, in Proceedings of the Linear Algebra for Large Scale and Real-Time Applications (Leuven, 1992), NATO Adv. Sci. Inst. Ser. E Appl. Sci. 232, Kluwer, Dordrecht, the Netherlands, 1993, pp. 293-314.
    • (1993) NATO Adv. Sci. Inst. Ser. E Appl. Sci. , vol.232 , pp. 293-314
    • Van Loan, C.F.1    Pitsianis, N.2
  • 45
    • 0000415334 scopus 로고    scopus 로고
    • A generalized one-dimensional fast multipole method with application to filtering of spherical harmonics
    • N. YARVIN AND V. ROKHLIN, A generalized one-dimensional fast multipole method with application to filtering of spherical harmonics, J. Comput. Phys., 147 (1998), pp. 594-609.
    • (1998) J. Comput. Phys. , vol.147 , pp. 594-609
    • Yarvin, N.1    Rokhlin, V.2
  • 46
    • 0003254417 scopus 로고
    • Sparse grids
    • Parallel Algorithms for Partial Differential Equations (Kiel, 1990), Vieweg, Braunschweig
    • C. ZENGER, Sparse grids, in Parallel Algorithms for Partial Differential Equations (Kiel, 1990), Notes Numer. Fluid Mech. 31, Vieweg, Braunschweig, 1991, pp. 241-251.
    • (1991) Notes Numer. Fluid Mech. 31 , pp. 241-251
    • Zenger, C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.