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Volumn 26, Issue 3, 2005, Pages 765-781

Quadrature rules based on the Arnoldi process

Author keywords

Bilinear form; Error estimate; Large scale problem; Quadrature method

Indexed keywords

BILINEAR FORM; ERROR ESTIMATE; LARGE-SCALE PROBLEM; QUADRATURE METHOD;

EID: 22944489601     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479803423822     Document Type: Article
Times cited : (15)

References (19)
  • 1
    • 0033098565 scopus 로고    scopus 로고
    • A computable error bound for matrix functional
    • D. CALVETTI, G. H. GOLUB, AND L. REICHEL, A computable error bound for matrix functional, J. Comput. Appl. Math., 103 (1999), pp. 301-306.
    • (1999) J. Comput. Appl. Math. , vol.103 , pp. 301-306
    • Calvetti, D.1    Golub, G.H.2    Reichel, L.3
  • 2
    • 0000924088 scopus 로고    scopus 로고
    • Estimation of the L-curve via Lanczos bidiagonalization
    • D. CALVETTI, G. H. GOLUB, AND L. REICHEL, Estimation of the L-curve via Lanczos bidiagonalization, BIT, 39 (1999), pp. 603-619.
    • (1999) BIT , vol.39 , pp. 603-619
    • Calvetti, D.1    Golub, G.H.2    Reichel, L.3
  • 4
    • 0034323326 scopus 로고    scopus 로고
    • Tikhonov regularization and the L-curve for large discrete ill-posed problems
    • D. CALVETTI, S. MORIGI, L. REICHEL, AND F. SGALLARI, Tikhonov regularization and the L-curve for large discrete ill-posed problems, J. Comput. Appl. Math., 123 (2000), pp. 423-446.
    • (2000) J. Comput. Appl. Math. , vol.123 , pp. 423-446
    • Calvetti, D.1    Morigi, S.2    Reichel, L.3    Sgallari, F.4
  • 5
    • 0034562121 scopus 로고    scopus 로고
    • Computable error bounds and estimates for the conjugate gradient method
    • D. CALVETTI, S. MORIGI, L. REICHEL, AND F. SGALLARI, Computable error bounds and estimates for the conjugate gradient method, Numer. Algorithms, 25 (2000), pp. 75-88.
    • (2000) Numer. Algorithms , vol.25 , pp. 75-88
    • Calvetti, D.1    Morigi, S.2    Reichel, L.3    Sgallari, F.4
  • 6
    • 0040687397 scopus 로고    scopus 로고
    • Application of anti-Gauss quadrature rules in linear algebra
    • W. Gautschi, G. H. Golub, and G. Opfer, eds., Birkhäuser-Verlag, Basel, Switzerland
    • D. CALVETTI, L. REICHEL, AND F. SGALLARI, Application of anti-Gauss quadrature rules in linear algebra, in Applications and Computation of Orthogonal Polynomials, W. Gautschi, G. H. Golub, and G. Opfer, eds., Birkhäuser-Verlag, Basel, Switzerland, 1999, pp. 41-56.
    • (1999) Applications and Computation of Orthogonal Polynomials , pp. 41-56
    • Calvetti, D.1    Reichel, L.2    Sgallari, F.3
  • 7
    • 0041590252 scopus 로고
    • Gauss quadratures associated with the Arnoldi process and the Lanczos algorithm
    • M. S. Moonen, G. H. Golub, and B. L. R. De Moor, eds., Kluwer, Dordrecht, The Netherlands
    • R. W. FREUND AND M. HOCHBRUCK, Gauss quadratures associated with the Arnoldi process and the Lanczos algorithm, in Linear Algebra for Large Scale and Real-Time Application, M. S. Moonen, G. H. Golub, and B. L. R. De Moor, eds., Kluwer, Dordrecht, The Netherlands, 1993, pp. 377-380.
    • (1993) Linear Algebra for Large Scale and Real-time Application , pp. 377-380
    • Freund, R.W.1    Hochbruck, M.2
  • 9
    • 0003093333 scopus 로고
    • Matrices, moments and quadrature
    • D. F. Griffiths and G. A. Watson, eds., Longman Scientific and Technical, Harlow, UK
    • G. H. GOLUB AND G. MEURANT, Matrices, moments and quadrature, in Numerical Analysis 1993, D. F. Griffiths and G. A. Watson, eds., Longman Scientific and Technical, Harlow, UK, 1994, pp. 105-156.
    • (1994) Numerical Analysis 1993 , pp. 105-156
    • Golub, G.H.1    Meurant, G.2
  • 10
    • 0000391978 scopus 로고    scopus 로고
    • Matrices, moments and quadrature II: How to compute the norm of the error in iterative methods
    • G. H. GOLUB AND G. MEURANT, Matrices, moments and quadrature II: How to compute the norm of the error in iterative methods, BIT, 37 (1997), pp. 687-705.
    • (1997) BIT , vol.37 , pp. 687-705
    • Golub, G.H.1    Meurant, G.2
  • 12
    • 0347799731 scopus 로고    scopus 로고
    • On Krylov subspace approximations to the matrix exponential operator
    • M. HOCHBRUCK AND C. LUBICH, On Krylov subspace approximations to the matrix exponential operator, SIAM J. Numer. Anal., 34 (1997), pp. 1911-1925.
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 1911-1925
    • Hochbruck, M.1    Lubich, C.2
  • 13
    • 0002658611 scopus 로고
    • Calculation of functions of unsymmetric matrices using Arnoldi's method
    • L. KNIZHNERMAN, Calculation of functions of unsymmetric matrices using Arnoldi's method, Comput. Math. Math. Phys., 31 (1991), pp. 1-9.
    • (1991) Comput. Math. Math. Phys. , vol.31 , pp. 1-9
    • Knizhnerman, L.1
  • 14
    • 0030352162 scopus 로고    scopus 로고
    • Anti-Gaussian quadrature formulas
    • D. P. LAURIE, Anti-Gaussian quadrature formulas, Math. Comp., 65 (1996), pp. 739-747.
    • (1996) Math. Comp. , vol.65 , pp. 739-747
    • Laurie, D.P.1
  • 15
    • 0042231879 scopus 로고    scopus 로고
    • The computation of bounds for the norm of the error in the conjugate gradient algorithm
    • G. MEURANT, The computation of bounds for the norm of the error in the conjugate gradient algorithm, Numer. Algorithms, 16 (1997), pp. 77-87.
    • (1997) Numer. Algorithms , vol.16 , pp. 77-87
    • Meurant, G.1
  • 17
    • 0035595411 scopus 로고    scopus 로고
    • Why Gaussian quadrature in the complex plane?
    • P. E. SAYLOR AND D. C. SMOLARSKI, Why Gaussian quadrature in the complex plane?, Numer. Algorithms, 26 (2001), pp. 251-280.
    • (2001) Numer. Algorithms , vol.26 , pp. 251-280
    • Saylor, P.E.1    Smolarski, D.C.2
  • 18
    • 23044529027 scopus 로고    scopus 로고
    • Addendum to: "Why Gaussian quadrature in the complex plane?,"
    • P. E. SAYLOR AND D. C. SMOLARSKI, Addendum to: "Why Gaussian quadrature in the complex plane?," Numer. Algorithms, 27 (2001), pp. 215-217.
    • (2001) Numer. Algorithms , vol.27 , pp. 215-217
    • Saylor, P.E.1    Smolarski, D.C.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.