메뉴 건너뛰기




Volumn 310, Issue 1-3, 2000, Pages 83-108

Superfast algorithms for Cauchy-like matrix computations and extensions

Author keywords

15A09; 47B35; 65F05; Cauchy like matrices; Displacement rank; Fast algorithms; Finite fields; Matrix factorization; Rational interpolation; Scaling rank

Indexed keywords


EID: 0034375299     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(00)00041-0     Document Type: Article
Times cited : (24)

References (55)
  • 1
    • 0000081585 scopus 로고
    • Asymptotically fast solution of Toeplitz and related systems of linear equations
    • Bitmead R.R., Anderson B.D.O. Asymptotically fast solution of Toeplitz and related systems of linear equations. Linear Algebra Appl. 34:1980;103-116.
    • (1980) Linear Algebra Appl. , vol.34 , pp. 103-116
    • Bitmead, R.R.1    Anderson, B.D.O.2
  • 4
    • 84968468488 scopus 로고
    • Solution of Vandermonde systems of equations
    • Björck A., Pereyra V. Solution of Vandermonde systems of equations. Math. Comp. 24:1970;893-903.
    • (1970) Math. Comp. , vol.24 , pp. 893-903
    • Björck, A.1    Pereyra, V.2
  • 5
    • 0347680470 scopus 로고
    • Mémorie sur les fonctions alternées et sur les somme alternées
    • Cauchy A.L. Mémorie sur les fonctions alternées et sur les somme alternées. Exercises d' Analyse et de Phys. Math. II:1841;151-159.
    • (1841) Exercises d' Analyse et de Phys. Math. , vol.2 , pp. 151-159
    • Cauchy, A.L.1
  • 6
    • 34249916280 scopus 로고
    • On fast multiplication of polynomials over arbitrary rings
    • Cantor D.G., Kaltofen E. On fast multiplication of polynomials over arbitrary rings. Acta Inf. 28(7):1991;697-701.
    • (1991) Acta Inf. , vol.28 , Issue.7 , pp. 697-701
    • Cantor, D.G.1    Kaltofen, E.2
  • 9
    • 0000006297 scopus 로고
    • A probabilistic remark on algebraic program testing
    • Demillo R.A., Lipton R.J. A probabilistic remark on algebraic program testing. Inform. Process. Lett. 7(4):1978;193-195.
    • (1978) Inform. Process. Lett. , vol.7 , Issue.4 , pp. 193-195
    • Demillo, R.A.1    Lipton, R.J.2
  • 10
    • 0040761796 scopus 로고
    • An inversion formula and fast algorithm for Cauchy-Vandermonde matrices
    • Fink T., Heinig G., Rost K. An inversion formula and fast algorithm for Cauchy-Vandermonde matrices. Linear Algebra Appl. 183:1993;179-191.
    • (1993) Linear Algebra Appl. , vol.183 , pp. 179-191
    • Fink, T.1    Heinig, G.2    Rost, K.3
  • 11
    • 0000082767 scopus 로고
    • Norm estimates for the inverses of Vandermonde matrices
    • Gautschi W. Norm estimates for the inverses of Vandermonde matrices. Numer. Math. 23:1975;337-347.
    • (1975) Numer. Math. , vol.23 , pp. 337-347
    • Gautschi, W.1
  • 13
    • 0040731675 scopus 로고
    • Inversion d'une matrice generalisant la matrice de Hilbert
    • Gastinel N. Inversion d'une matrice generalisant la matrice de Hilbert. Chiffres. 3:1960;149-152.
    • (1960) Chiffres , vol.3 , pp. 149-152
    • Gastinel, N.1
  • 14
    • 84966207762 scopus 로고
    • A fast algorithm for the multiplication of generalized Hilbert matrices with vectors
    • Gerasoulis A. A fast algorithm for the multiplication of generalized Hilbert matrices with vectors. Math. Comp. 50(181):1987;179-188.
    • (1987) Math. Comp. , vol.50 , Issue.181 , pp. 179-188
    • Gerasoulis, A.1
  • 15
    • 0002759667 scopus 로고
    • Efficient solution of linear systems of equations with recursive structure
    • Gohberg I., Kailath T., Koltracht I. Efficient solution of linear systems of equations with recursive structure. Linear Algebra Appl. 80:1986;81-113.
    • (1986) Linear Algebra Appl. , vol.80 , pp. 81-113
    • Gohberg, I.1    Kailath, T.2    Koltracht, I.3
  • 16
    • 0003044834 scopus 로고
    • Linear complexity parallel algorithms for linear systems of equations with recursive structure
    • Gohberg I., Kailath T., Koltracht I., Lancaster P. Linear complexity parallel algorithms for linear systems of equations with recursive structure. Linear Algebra Appl. 88/89:1987;271-315.
    • (1987) Linear Algebra Appl. , vol.8889 , pp. 271-315
    • Gohberg, I.1    Kailath, T.2    Koltracht, I.3    Lancaster, P.4
  • 17
    • 84968505008 scopus 로고
    • Fast Gausian elimination with partial pivoting for matrices with displacement structure
    • Gohberg I., Kailath T., Olshevsky V. Fast Gausian elimination with partial pivoting for matrices with displacement structure. Math. Comp. 64:1995;1557-1576.
    • (1995) Math. Comp. , vol.64 , pp. 1557-1576
    • Gohberg, I.1    Kailath, T.2    Olshevsky, V.3
  • 18
    • 0004236492 scopus 로고
    • Johns Hopkins University Press, Baltimore, MD, (second ed.), (third ed.)
    • G.H. Golub, C.F. Van Loan, Matrix Computations, Johns Hopkins University Press, Baltimore, MD, 1989 (second ed.), 1996 (third ed.).
    • (1989) Matrix Computations
    • Golub, G.H.1    Van Loan, C.F.2
  • 19
    • 38149147254 scopus 로고
    • Complexity of multiplication with vectors for structured matrices
    • Gohberg I., Olshevsky V. Complexity of multiplication with vectors for structured matrices. Linear Algebra Appl. 202:1994;163-192.
    • (1994) Linear Algebra Appl. , vol.202 , pp. 163-192
    • Gohberg, I.1    Olshevsky, V.2
  • 20
    • 0000376665 scopus 로고
    • Fast algorithms with preprocessing for matrix-vector multiplication problems
    • Gohberg I., Olshevsky V. Fast algorithms with preprocessing for matrix-vector multiplication problems. J. Complexity. 10(4):1994;411-427.
    • (1994) J. Complexity , vol.10 , Issue.4 , pp. 411-427
    • Gohberg, I.1    Olshevsky, V.2
  • 21
    • 0001926832 scopus 로고
    • Fast state space algorithms for matrix Nehari and Nehari-Takagi interpolation problems
    • Gohberg I., Olshevsky V. Fast state space algorithms for matrix Nehari and Nehari-Takagi interpolation problems. Integral Equations Operator Theory. 20(1):1994;44-83.
    • (1994) Integral Equations Operator Theory , vol.20 , Issue.1 , pp. 44-83
    • Gohberg, I.1    Olshevsky, V.2
  • 22
    • 0041557124 scopus 로고    scopus 로고
    • Fast inversion of Vandermonde and Vandermonde-like matrices
    • in: A. Paulraj, V. Roychowdhury, C. Shaper (Eds.), Kluwer Academic Publisher, Dordrecht
    • I. Gohberg, V. Olshevsky, Fast inversion of Vandermonde and Vandermonde-like matrices, in: A. Paulraj, V. Roychowdhury, C. Shaper (Eds.), Communications, Computation, Control and Signal Processing: A Tribute to Thomas Kailath, Kluwer Academic Publisher, Dordrecht, 1996, pp. 205-221.
    • (1996) Communications, Computation, Control and Signal Processing: A Tribute to Thomas Kailath , pp. 205-221
    • Gohberg, I.1    Olshevsky, V.2
  • 23
    • 0000396658 scopus 로고
    • A fast algorithm for particle simulation
    • Greengard L., Rokhlin V. A fast algorithm for particle simulation. J. Comput. Phys. 73(2):1987;325-348.
    • (1987) J. Comput. Phys. , vol.73 , Issue.2 , pp. 325-348
    • Greengard, L.1    Rokhlin, V.2
  • 24
    • 0012063613 scopus 로고
    • Fast solution of Vandermonde-like systems involving orthogonal polynomials
    • Higham N.J. Fast solution of Vandermonde-like systems involving orthogonal polynomials. IMAJ. Numer. Anal. 8:1988;473-486.
    • (1988) IMAJ. Numer. Anal. , vol.8 , pp. 473-486
    • Higham, N.J.1
  • 25
    • 0001939091 scopus 로고
    • Stability analysis of algorithm for solving confluent Vandermonde-like systems
    • Higham N.J. Stability analysis of algorithm for solving confluent Vandermonde-like systems. SIAM J. Matrix Anal. Appl. 11:1990;23-41.
    • (1990) SIAM J. Matrix Anal. Appl. , vol.11 , pp. 23-41
    • Higham, N.J.1
  • 27
    • 0002675246 scopus 로고
    • Algebraic methods for Toeplitz-like matrices and operators
    • Birkhäuser, Basel
    • H. Heinig, K. Rost, Algebraic methods for Toeplitz-like matrices and operators, Operator Theory, vol. 13, Birkhäuser, Basel, 1984.
    • (1984) Operator Theory , vol.13
    • Heinig, H.1    Rost, K.2
  • 28
    • 0005296761 scopus 로고
    • Asymptotically fast solution of Toeplitz-like singular linear systems
    • ACM Press, New York
    • E. Kaltofen, Asymptotically fast solution of Toeplitz-like singular linear systems, Proc. ACM-SIGSAM Intern. Symp. on Symbolic and Alg. Comp., ACM Press, New York, 1994, pp. 297-304.
    • (1994) Proc. ACM-SIGSAM Intern. Symp. on Symbolic and Alg. Comp. , pp. 297-304
    • Kaltofen, E.1
  • 29
    • 84968492714 scopus 로고
    • Analysis of Coppersmith's block Wiedemann algorithm for the parallel solution of sparse linear systems
    • Kaltofen E. Analysis of Coppersmith's block Wiedemann algorithm for the parallel solution of sparse linear systems. Math. Comp. 64(210):1995;777-806.
    • (1995) Math. Comp. , vol.64 , Issue.210 , pp. 777-806
    • Kaltofen, E.1
  • 30
    • 0017951648 scopus 로고
    • Displacement ranks of matrices and linear equations
    • Kailath T., Kung S.Y., Morf M. Displacement ranks of matrices and linear equations. J. Math. Anal. Appl. 68(2):1979;395-407.
    • (1979) J. Math. Anal. Appl. , vol.68 , Issue.2 , pp. 395-407
    • Kailath, T.1    Kung, S.Y.2    Morf, M.3
  • 32
    • 21844484490 scopus 로고
    • Fast solution of confluent Vandermonde linear systems
    • Lu H. Fast solution of confluent Vandermonde linear systems. SIAM J. Matrix Anal. Appl. 15(4):1994;1277-1289.
    • (1994) SIAM J. Matrix Anal. Appl. , vol.15 , Issue.4 , pp. 1277-1289
    • Lu, H.1
  • 33
    • 21844485255 scopus 로고
    • Fast algorithms for confluent Vandermonde linear systems and generalized Trummer's problem
    • Lu H. Fast algorithms for confluent Vandermonde linear systems and generalized Trummer's problem. SIAM J. Matrix Anal. Appl. 16(2):1995;655-674.
    • (1995) SIAM J. Matrix Anal. Appl. , vol.16 , Issue.2 , pp. 655-674
    • Lu, H.1
  • 34
    • 0030552749 scopus 로고    scopus 로고
    • Solution of Vandermonde-like systems and confluent Vandermonde-like systems
    • Lu H. Solution of Vandermonde-like systems and confluent Vandermonde-like systems. SIAMJ. Matrix Anal. Appl. 17(1):1996;127-138.
    • (1996) SIAMJ. Matrix Anal. Appl. , vol.17 , Issue.1 , pp. 127-138
    • Lu, H.1
  • 35
    • 0003420247 scopus 로고
    • Ph.D. Thesis, Department of Electrical Engineering, Stanford University, Stanford, CA
    • M. Morf, Fast algorithms for multivariable systems, Ph.D. Thesis, Department of Electrical Engineering, Stanford University, Stanford, CA, 1974.
    • (1974) Fast Algorithms for Multivariable Systems
    • Morf, M.1
  • 36
    • 0000692349 scopus 로고    scopus 로고
    • Multivariate polynomials, duality and structured matrices
    • B. Mourrain, V.Y. Pan, Multivariate polynomials, duality and structured matrices, J. Complexity 16 (1) 2000.
    • (2000) J. Complexity 16 , vol.1
    • Mourrain, B.1    Pan, V.Y.2
  • 37
    • 0019146429 scopus 로고
    • Doubling algorithms for Toeplitz and related equations
    • in: IEEE Computer Society Press, Silver Spring, MD
    • M. Morf, Doubling algorithms for Toeplitz and related equations, in: Proceedings of the IEEE International Conference on ASSP, IEEE Computer Society Press, Silver Spring, MD, 1980, pp. 954-959.
    • (1980) Proceedings of the IEEE International Conference on ASSP , pp. 954-959
    • Morf, M.1
  • 38
    • 0032319031 scopus 로고    scopus 로고
    • A unified superfast algorithm for boundary rational tangential interpolation problem and for inversion and factorization of dense structured matrices
    • in: IEEE Computer Society Press, Silver Spring, MD, October
    • V. Olshevsky, V.Y. Pan, A unified superfast algorithm for boundary rational tangential interpolation problem and for inversion and factorization of dense structured matrices, in: Proceedings of the 39th Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, Silver Spring, MD, October 1998, pp. 192-201.
    • (1998) Proceedings of the 39th Annual IEEE Symposium on Foundations of Computer Science , pp. 192-201
    • Olshevsky, V.1    Pan, V.Y.2
  • 41
    • 84903946746 scopus 로고
    • On computations with dense structured matrices
    • ACM Press, New York
    • V.Y. Pan, On computations with dense structured matrices, Proc. ACM-SIGSAM Intern. Symp. on Symbolic and Alg. Comp., ACM Press, New York, 1989, pp. 34-42. Math. Comp. 55 (191) (1990) 179-190.
    • (1989) Proc. ACM-SIGSAM Intern. Symp. on Symbolic and Alg. Comp. , pp. 34-42
    • Pan, V.Y.1
  • 42
    • 84966229708 scopus 로고
    • V.Y. Pan, On computations with dense structured matrices, Proc. ACM-SIGSAM Intern. Symp. on Symbolic and Alg. Comp., ACM Press, New York, 1989, pp. 34-42. Math. Comp. 55 (191) (1990) 179-190.
    • (1990) Math. Comp. , vol.55 , Issue.191 , pp. 179-190
  • 43
    • 38249008425 scopus 로고
    • Parametrization of Newton's iteration for computations with structured matrices and applications
    • V.Y. Pan, Parametrization of Newton's iteration for computations with structured matrices and applications, Comput. Math. (with Appl.) 24 (3) (1992) 61-75.
    • (1992) Comput. Math. (With Appl.) , vol.24 , Issue.3 , pp. 61-75
    • Pan, V.Y.1
  • 44
    • 21144462386 scopus 로고
    • Decreasing the displacement rank of a matrix
    • Pan V.Y. Decreasing the displacement rank of a matrix. SIAM J. Matrix Anal. Appl. 14(1):1993;118-121.
    • (1993) SIAM J. Matrix Anal. Appl. , vol.14 , Issue.1 , pp. 118-121
    • Pan, V.Y.1
  • 46
    • 0033874758 scopus 로고    scopus 로고
    • Nearly optimal computations with structured matrices
    • in: ACM Press, New York, and SIAM Publications, Philadelphia, PA
    • V.Y. Pan, Nearly optimal computations with structured matrices, in: Proceedings of the 11th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'2000), ACM Press, New York, and SIAM Publications, Philadelphia, PA, 2000, pp. 953-962.
    • (2000) Proceedings of the 11th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'2000) , pp. 953-962
    • Pan, V.Y.1
  • 50
    • 0007428490 scopus 로고
    • A matrix problem with application to rapid solution of integral equations
    • Reichel L. A matrix problem with application to rapid solution of integral equations. SIAM J. Sci. Statist. Comput. 11:1990;263-280.
    • (1990) SIAM J. Sci. Statist. Comput. , vol.11 , pp. 263-280
    • Reichel, L.1
  • 51
    • 46549096170 scopus 로고
    • Rapid solution of integral equations of classical potential theory
    • Rokhlin F. Rapid solution of integral equations of classical potential theory. J. Comput. Phys. 60:1985;187-207.
    • (1985) J. Comput. Phys. , vol.60 , pp. 187-207
    • Rokhlin, F.1
  • 52
    • 84976779342 scopus 로고
    • Fast probabilistic algorithms for verification of polynomial identities
    • Schwartz J.T. Fast probabilistic algorithms for verification of polynomial identities. J. ACM. 27(4):1980;701-717.
    • (1980) J. ACM , vol.27 , Issue.4 , pp. 701-717
    • Schwartz, J.T.1
  • 53
    • 34250487811 scopus 로고
    • Gaussian elimination is not optimal
    • Strassen V. Gaussian elimination is not optimal. Numer. Math. 13:1969;354-356.
    • (1969) Numer. Math. , vol.13 , pp. 354-356
    • Strassen, V.1
  • 54
    • 0022769618 scopus 로고
    • An efficient implementation of a conformal mapping method using the Szegö kernel
    • Trummer M. An efficient implementation of a conformal mapping method using the Szegö kernel. SIAM J. Numer. Anal. 23:1986;853-872.
    • (1986) SIAM J. Numer. Anal. , vol.23 , pp. 853-872
    • Trummer, M.1
  • 55
    • 84925463455 scopus 로고
    • Probabilistic Algorithm for Sparse Polynominals
    • Springer, Berlin
    • R.Z. Zippel, Probabilistic Algorithm for Sparse Polynominals, Proc. EUROSAM 79, Lecture Notes in Computer Science, vol. 72, Springer, Berlin, 1979, pp. 216-226.
    • (1979) Proc. EUROSAM 79, Lecture Notes in Computer Science , vol.72 , pp. 216-226
    • Zippel, R.Z.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.