Počet záznamů: 1  

Error Estimation in Preconditioned Conjugate Gradients

  1. 1.
    0405612 - UIVT-O 330994 RIV SE eng J - Článek v odborném periodiku
    Strakoš, Zdeněk - Tichý, Petr
    Error Estimation in Preconditioned Conjugate Gradients.
    [Odhady chyb v přepodmíněné metodě konjugovaných gradientů.]
    Bit. Roč. 45, - (2005), s. 789-817. ISSN 0006-3835. E-ISSN 1572-9125
    Grant CEP: GA AV ČR 1ET400300415; GA AV ČR KJB1030306
    Výzkumný záměr: CEZ:AV0Z10300504
    Klíčová slova: preconditioned conjugate gradient method * error bounds * stopping criteria * evaluation of convergence * numerical stability * finite precision arithmetic * rounding errors
    Kód oboru RIV: BA - Obecná matematika
    Impakt faktor: 0.509, rok: 2005

    Citováno: 28

    --- SIMONCINI, V. - SZYLD, D.B. Recent computational developments in Krylov subspace methods for linear systems. NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS. ISSN 1070-5325, FEB 2007, vol. 14, no. 1, p. 1-59. [WOS]
    --- Meurant, G., The Lanczos and conjugate gradient algorithms. From theory to finite precision computations. Software, Environments, and Tools, 19. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2006
    --- ARIOLI, M. - MANZINI, G. A network programming approach in solving Darcy's equations by mixed finite-element methods. ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS. ISSN 1068-9613, 2006, vol. 22, p. 41-70. [WOS]
    --- GOLUB, G.H. - STOLL, M. - WATHEN, A. APPROXIMATION OF THE SCATTERING AMPLITUDE AND LINEAR SYSTEMS. ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS. ISSN 1068-9613, 2008, vol. 31, p. 178-203. [WOS]
    --- BOUYOULI, R. - MEURANT, G. - SMOCH, L. - SADOK, H. New results on the convergence of the conjugate gradient method. NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS. ISSN 1070-5325, MAR 2009, vol. 16, no. 3, p. 223-236. [WOS]
    --- ALIAGA, J.I. - BOLLHOFER, M. - MARTIN, A.F. - QUINTANA-ORTI, E.S. Design, Tuning and Evaluation of Parallel Multilevel ILU Preconditioners. HIGH PERFORMANCE COMPUTING FOR COMPUTATIONAL SCIENCE - VECPAR 2008. ISSN 0302-9743, 2008, vol. 5336, p. 314-327. [WOS]
    --- DANILOV, D. - MAGNUS, J.R. On the estimation of a large sparse Bayesian system: The Snaer program. COMPUTATIONAL STATISTICS & DATA ANALYSIS. ISSN 0167-9473, MAY 15 2008, vol. 52, no. 9, p. 4203-4224. [WOS]
    --- FROMMER, A. - SIMONCINI, V. Stopping criteria for rational matrix functions of Hermitian and symmetric matrices. SIAM JOURNAL ON SCIENTIFIC COMPUTING. ISSN 1064-8275, 2007, vol. 30, no. 3, p. 1387-1412. [WOS]
    --- FRAYSSE, V. - GIRAUD, L. - GRATTON, S. A set of flexible GMRES routines for real and complex arithmetics on high-performance computers. ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE. ISSN 0098-3500, JUL 2008, vol. 35, no. 2. [WOS]
    --- ALIAGA, J.I. - BOLLHOFER, M. - MARTIN, A.F. - QUINTANA-ORTI, E.S. Exploiting thread-level parallelism in the iterative solution of sparse linear systems. PARALLEL COMPUTING. ISSN 0167-8191, MAR 2011, vol. 37, no. 3, p. 183-202. [WOS]
    --- JIRANEK, P. - TITLEY-PELOQUIN, D. ESTIMATING THE BACKWARD ERROR IN LSQR. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS. ISSN 0895-4798, 2010, vol. 31, no. 4, p. 2055-2074. [WOS]
    --- GOLUB, G.H. - MEURANT, G. Matrices, Moments and Quadrature with Applications. MATRICES, MOMENTS AND QUADRATURE WITH APPLICATIONS. 2010, p. 1-363. [WOS]
    --- DOLEJSI, V. - SEBESTOVA, I. - VOHRALIK, M. Algebraic and Discretization Error Estimation by Equilibrated Fluxes for Discontinuous Galerkin Methods on Nonmatching Grids. JOURNAL OF SCIENTIFIC COMPUTING. ISSN 0885-7474, JUL 2015, vol. 64, no. 1, p. 1-34. [WOS]
    --- HERZOG, R. - SACHS, E. SUPERLINEAR CONVERGENCE OF KRYLOV SUBSPACE METHODS FOR SELF-ADJOINT PROBLEMS IN HILBERT SPACE. SIAM JOURNAL ON NUMERICAL ANALYSIS. ISSN 0036-1429, 2015, vol. 53, no. 3, p. 1304-1324. [WOS]
    --- DU, L. - FUTAMURA, Y. - SAKURAI, T. Block conjugate gradient type methods for the approximation of bilinear form C(H)A(-1)B. COMPUTERS & MATHEMATICS WITH APPLICATIONS. ISSN 0898-1221, JAN 2014, vol. 66, no. 12, p. 2446-2455. [WOS]
    --- ZLATEV, Z. - GEORGIEV, K. Applying approximate LU-factorizations as preconditioners in eight iterative methods for solving systems of linear algebraic equations. CENTRAL EUROPEAN JOURNAL OF MATHEMATICS. ISSN 1895-1074, AUG 2013, vol. 11, no. 8, p. 1510-1530. [WOS]
    --- FROMMER, A. - KAHL, K. - LIPPERT, T. - RITTICH, H. 2-NORM ERROR BOUNDS AND ESTIMATES FOR LANCZOS APPROXIMATIONS TO LINEAR SYSTEMS AND RATIONAL MATRIX FUNCTIONS. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS. ISSN 0895-4798, 2013, vol. 34, no. 3, p. 1046-1065. [WOS]
    --- ARIOLI, M. GENERALIZED GOLUB-KAHAN BIDIAGONALIZATION AND STOPPING CRITERIA. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS. ISSN 0895-4798, 2013, vol. 34, no. 2, p. 571-592. [WOS]
    --- ARIOLI, M. - GRATTON, S. Linear regression models, least-squares problems, normal equations, and stopping criteria for the conjugate gradient method. COMPUTER PHYSICS COMMUNICATIONS. ISSN 0010-4655, NOV 2012, vol. 183, no. 11, p. 2322-2336. [WOS]
    --- GEORGIEV, K. - ZLATEV, Z. Numerical Experiments with Applying Approximate LU-factorizations as Preconditioners for Solving SLAEs with Coefficient Matrices from the "Sparse Matrix Market". APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES. ISSN 0094-243X, 2012, vol. 1487, p. 104-111. [WOS]
    --- ROBINI, M. - ZHU, Y.M. - LV, X.D. - LIU, W.Y. INEXACT HALF-QUADRATIC OPTIMIZATION FOR IMAGE RECONSTRUCTION. 2016 IEEE INTERNATIONAL CONFERENCE ON IMAGE PROCESSING (ICIP). ISSN 1522-4880, 2016, p. 3513-3517. [WOS]
    --- LUBKOLL, L. - SCHIELA, A. - WEISER, M. An affine covariant composite step method for optimization with PDEs as equality constraints. OPTIMIZATION METHODS & SOFTWARE. ISSN 1055-6788, 2017, vol. 32, no. 5, p. 1132-1161. [WOS]
    --- BASTIAN, P. - MULLER, E.H. - MUTHING, S. - PIATKOWSKI, M. Matrix-free multigrid block-preconditioners for higher order discontinuous Galerkin discretisations. JOURNAL OF COMPUTATIONAL PHYSICS. ISSN 0021-9991, OCT 1 2019, vol. 394, p. 417-439. [WOS]
    --- COOLS, S. Analyzing and improving maximal attainable accuracy in the communication hiding pipelined BiCGStab method. PARALLEL COMPUTING. ISSN 0167-8191, AUG 2019, vol. 86, p. 16-35. [WOS]
    --- PAPEZ, J. - GRIGORI, L. - STOMPOR, R. Solving linear equations with messenger-field and conjugate gradient techniques: An application to CMB data analysis. ASTRONOMY & ASTROPHYSICS. ISSN 1432-0746, NOV 29 2018, vol. 620. [WOS]
    --- ROBINI, M.C. - YANG, F. - ZHU, Y.M. Inexact Half-Quadratic Optimization for Linear Inverse Problems. SIAM JOURNAL ON IMAGING SCIENCES. ISSN 1936-4954, 2018, vol. 11, no. 2, p. 1078-1133. [WOS]
    --- COOLS, S. - YETKIN, E.F. - AGULLO, E. - GIRAUD, L. - VANROOSE, W. ANALYZING THE EFFECT OF LOCAL ROUNDING ERROR PROPAGATION ON THE MAXIMAL ATTAINABLE ACCURACY OF THE PIPELINED CONJUGATE GRADIENT METHOD. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS. ISSN 0895-4798, 2018, vol. 39, no. 1, p. 426-450. [WOS]
    --- SPILLANE, N. Algebraic Adaptive Multipreconditioning Applied to Restricted Additive Schwarz. DOMAIN DECOMPOSITION METHODS IN SCIENCE AND ENGINEERING XXIII. ISSN 1439-7358, 2017, vol. 116, p. 93-104. [WOS]

    Trvalý link: http://hdl.handle.net/11104/0125762
    Název souboruStaženoVelikostKomentářVerzePřístup
    0405612.pdf01.7 MBAutorský preprintpovolen
     

Počet záznamů: 1  

  Tyto stránky využívají soubory cookies, které usnadňují jejich prohlížení. Další informace o tom jak používáme cookies.