메뉴 건너뛰기




Volumn 343, Issue , 2002, Pages 233-265

Structured matrices and Newton's iteration: Unified approach

Author keywords

Displacement rank; Inverse displacement operators; Newton's iteration for matrix inversion; Structured matrices

Indexed keywords

INVERSE PROBLEMS; ITERATIVE METHODS;

EID: 84924422763     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(01)00336-6     Document Type: Article
Times cited : (40)

References (42)
  • 1
    • 0000111043 scopus 로고
    • A variant of the Gohberg-Semencul formula involving circulant matrices
    • G.S. Ammar, and P. Gader A variant of the Gohberg-Semencul formula involving circulant matrices SIAM J. Matrix Anal. Appl. 12 3 1991 534 541
    • (1991) SIAM J. Matrix Anal. Appl. , vol.12 , Issue.3 , pp. 534-541
    • Ammar, G.S.1    Gader, P.2
  • 3
    • 21144476055 scopus 로고
    • Improved parallel computations with Toeplitz-like and Hankel-like matrices
    • D. Bini, and V.Y. Pan Improved parallel computations with Toeplitz-like and Hankel-like matrices Linear Algebra Appl. 188/189 1993 3 29
    • (1993) Linear Algebra Appl. , vol.188-189 , pp. 3-29
    • Bini, D.1    Pan, V.Y.2
  • 5
    • 0030246195 scopus 로고    scopus 로고
    • Conjugate gradient methods for Toeplitz systems
    • R.H. Chan, and M.K. Ng Conjugate gradient methods for Toeplitz systems SIAM Rev. 38 1996 427 482
    • (1996) SIAM Rev. , vol.38 , pp. 427-482
    • Chan, R.H.1    Ng, M.K.2
  • 6
    • 84968505008 scopus 로고
    • Fast Gaussian elimination with partial pivoting for matrices with displacement structure
    • I. Gohberg, T. Kailath, and V. Olshevsky Fast Gaussian elimination with partial pivoting for matrices with displacement structure Math. Comput. 64 1995 1557 1576
    • (1995) Math. Comput. , vol.64 , pp. 1557-1576
    • Gohberg, I.1    Kailath, T.2    Olshevsky, V.3
  • 7
    • 0004236492 scopus 로고    scopus 로고
    • third ed. Johns Hopkins University Press Baltimore, MD
    • G.H. Golub, and C.F. Van Loan Matrix Computations third ed. 1996 Johns Hopkins University Press Baltimore, MD
    • (1996) Matrix Computations
    • Golub, G.H.1    Van Loan, C.F.2
  • 8
  • 9
    • 38149147254 scopus 로고
    • Complexity of multiplication with vectors for structured matrices
    • I. Gohberg, and V. Olshevsky 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
  • 10
    • 0001726473 scopus 로고
    • On the inversion of finite Toeplitz matrices and their continuous analogs
    • I. Gohberg, and A. Semencul On the inversion of finite Toeplitz matrices and their continuous analogs Mat. Issled. 2 1972 187 224
    • (1972) Mat. Issled. , vol.2 , pp. 187-224
    • Gohberg, I.1    Semencul, A.2
  • 11
    • 0001301897 scopus 로고
    • Newton's method for the matrix square root
    • N.J. Higham Newton's method for the matrix square root Math. Comput. 46 1986 537 550
    • (1986) Math. Comput. , vol.46 , pp. 537-550
    • Higham, N.J.1
  • 12
    • 0001692403 scopus 로고
    • Computing the polar decomposition - With applications
    • N.J. Higham Computing the polar decomposition - with applications SIAM J. Sci. Statist. Comput. 7 4 1986 1160 1174
    • (1986) SIAM J. Sci. Statist. Comput. , vol.7 , Issue.4 , pp. 1160-1174
    • Higham, N.J.1
  • 13
    • 0012063613 scopus 로고
    • Fast solution of Vandermonde-like systems involving orthogonal polynomials
    • N.J. Higham Fast solution of Vandermonde-like systems involving orthogonal polynomials IMA J. Numer. Anal. 8 1988 473 486
    • (1988) IMA J. Numer. Anal. , vol.8 , pp. 473-486
    • Higham, N.J.1
  • 14
    • 0348188053 scopus 로고
    • The matrix sign decomposition and its relations to polar decomposition
    • N.J. Higham The matrix sign decomposition and its relations to polar decomposition Linear Algebra Appl. 212/213 1994 3 20
    • (1994) Linear Algebra Appl. , vol.212-213 , pp. 3-20
    • Higham, N.J.1
  • 16
    • 0002675246 scopus 로고
    • Algebraic methods for Toeplitz-like matrices and operators
    • I. Gohberg, (Ed.) Birkhäuser, Basel
    • G. Heinig, K. Rost, Algebraic methods for Toeplitz-like matrices and operators, in: I. Gohberg, (Ed.), Operator Theory: Advances and Applications, vol. 13, Birkhäuser, Basel, 1984
    • (1984) Operator Theory: Advances and Applications , vol.13
    • Heinig, G.1    Rost, K.2
  • 18
    • 0017951648 scopus 로고
    • Displacement ranks of matrices and linear equations
    • T. Kailath, S.Y. Kung, and M. Morf 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
  • 19
    • 0000204992 scopus 로고
    • On scaling Newton's method for polar decomposition and the matrix sign function
    • C. Kenney, and A.J. Laub On scaling Newton's method for polar decomposition and the matrix sign function SIAM J Matrix Anal. Appl. 13 3 1992 698 706
    • (1992) SIAM J Matrix Anal. Appl. , vol.13 , Issue.3 , pp. 698-706
    • Kenney, C.1    Laub, A.J.2
  • 20
    • 0029715230 scopus 로고    scopus 로고
    • Displacement structure approach to discrete transform based preconditioners of G. Strang type and of T. Chan type
    • T. Kailath, and V. Olshevsky Displacement structure approach to discrete transform based preconditioners of G. Strang type and of T. Chan type Calcolo 33 1996 191 208
    • (1996) Calcolo , vol.33 , pp. 191-208
    • Kailath, T.1    Olshevsky, V.2
  • 21
    • 84924355356 scopus 로고    scopus 로고
    • Displacement structure approach to polynomial Vandermonde and related matrices
    • T. Kailath, and V. Olshevsky Displacement structure approach to polynomial Vandermonde and related matrices Linear Algebra Appl. 285 1997 37 67
    • (1997) Linear Algebra Appl. , vol.285 , pp. 37-67
    • Kailath, T.1    Olshevsky, V.2
  • 23
    • 0030552749 scopus 로고    scopus 로고
    • Solution of Vandermonde-like systems and confluent Vandermonde-like systems
    • H. Lu Solution of Vandermonde-like systems and confluent Vandermonde-like systems SIAM J. Matrix Anal. Appl. 17 1 1996 127 138
    • (1996) SIAM J. Matrix Anal. Appl. , vol.17 , Issue.1 , pp. 127-138
    • Lu, H.1
  • 24
    • 0032319031 scopus 로고    scopus 로고
    • A unified superfast algorithm for boundary rational tangential interpolation problem and for inversion and factorization of dense structured matrices
    • IEEE Computer Society Press
    • 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, 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
  • 26
    • 84966229708 scopus 로고
    • On computations with dense structured matrices
    • V.Y. Pan On computations with dense structured matrices Math. Comput. 55 191 1990 179 190
    • (1990) Math. Comput. , vol.55 , Issue.191 , pp. 179-190
    • Pan, V.Y.1
  • 27
    • 38249015327 scopus 로고
    • Parallel solution of Toeplitz-like linear systems
    • V.Y. Pan Parallel solution of Toeplitz-like linear systems J. Complexity 8 1992 1 21
    • (1992) J. Complexity , vol.8 , pp. 1-21
    • Pan, V.Y.1
  • 28
    • 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. Appl. 24 3 1992 61 75
    • (1992) Comput. Math. Appl. , vol.24 , Issue.3 , pp. 61-75
    • Pan, V.Y.1
  • 29
    • 21144462386 scopus 로고
    • Decreasing the displacement rank of a matrix
    • V.Y. Pan 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
  • 30
    • 0027595846 scopus 로고
    • Concurrent iterative algorithm for Toepliz-like linear systems
    • V.Y. Pan Concurrent iterative algorithm for Toepliz-like linear systems IEEE Trans. Parallel and Distributed Systems 4 5 1993 592 600
    • (1993) IEEE Trans. Parallel and Distributed Systems , vol.4 , Issue.5 , pp. 592-600
    • Pan, V.Y.1
  • 35
    • 38249004086 scopus 로고
    • A new approach to fast polynomial interpolation and multipoint evaluation
    • V.Y. Pan, E. Landowne, A. Sadikou, and O. Tiga A new approach to fast polynomial interpolation and multipoint evaluation Comput. Math. Appl. 25 9 1993 25 30
    • (1993) Comput. Math. Appl. , vol.25 , Issue.9 , pp. 25-30
    • Pan, V.Y.1    Landowne, E.2    Sadikou, A.3    Tiga, O.4
  • 36
    • 27644515683 scopus 로고    scopus 로고
    • Newton's iteration for the inversion of structured matrices
    • D. Bini, E. Tyrtyshnikov, P. Yalamov, Nova Science Publishers USA
    • V.Y. Pan, and Y. Rami Newton's iteration for the inversion of structured matrices D. Bini, E. Tyrtyshnikov, P. Yalamov, Structured Matrices: Recent Developments in Theory and Computation 2001, pp. 79-90 Nova Science Publishers USA
    • (2001) Structured Matrices: Recent Developments in Theory and Computation , pp. 79-90
    • Pan, V.Y.1    Rami, Y.2
  • 38
    • 0012063917 scopus 로고
    • An improved Newton iteration for the generalized inverse of a matrix, with applications
    • V.Y. Pan, and R. Schreiber An improved Newton iteration for the generalized inverse of a matrix, with applications SIAM J. Sci. Statist. Comput. 12 5 1991 1109 1131
    • (1991) SIAM J. Sci. Statist. Comput. , vol.12 , Issue.5 , pp. 1109-1131
    • Pan, V.Y.1    Schreiber, R.2
  • 40
    • 0031101947 scopus 로고    scopus 로고
    • Newton's iteration for inversion of Cauchy-like and other structured matrices
    • V.Y. Pan, A. Zheng, X. Huang, and O. Dias Newton's iteration for inversion of Cauchy-like and other structured matrices J. Complexity 13 1997 108 124
    • (1997) J. Complexity , vol.13 , pp. 108-124
    • Pan, V.Y.1    Zheng, A.2    Huang, X.3    Dias, O.4
  • 41
    • 0003838237 scopus 로고    scopus 로고
    • Fast multipoint polynomial evaluation and interpolation via computations with structured matrices
    • V.Y. Pan, A. Zheng, X. Huang, and Y. Yu Fast multipoint polynomial evaluation and interpolation via computations with structured matrices Ann. Numer. Math. 4 1997 483 510
    • (1997) Ann. Numer. Math. , vol.4 , pp. 483-510
    • Pan, V.Y.1    Zheng, A.2    Huang, X.3    Yu, Y.4
  • 42
    • 21144469538 scopus 로고
    • Product rules for the displacement of nearly-Toeplitz matrices
    • D.H. Wood Product rules for the displacement of nearly-Toeplitz matrices Linear Algebra Appl. 188 1993 641 663
    • (1993) Linear Algebra Appl. , vol.188 , pp. 641-663
    • Wood, D.H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.