Accuracy and effectiveness of preconditioned conjugate gradient algorithms for large and ill-conditioned problems

DOI10.1016/0045-7825(93)90079-DzbMath0845.73072OpenAlexW2019910246MaRDI QIDQ1912189

Manolis Papadrakakis, N. Bitoulas

Publication date: 6 May 1996

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0045-7825(93)90079-d

zbMATH Keywords

iterative refinement schememixed precision calculations

Mathematics Subject Classification ID

Finite element methods applied to problems in solid mechanics (74S05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

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Cites Work

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• On the real convergence rate of the conjugate gradient method
• SIRT- and CG-type methods for the iterative solution of sparse linear least-squares problems
• On the rate of convergence of the preconditioned conjugate gradient method
• The rate of convergence of conjugate gradients
• Roundoff-error analysis of a new class of conjugate-gradient algorithms
• Guidelines for the usage of incomplete decompositions in solving sets of linear equations as they occur in practical problems
• On numerical error in the finite element method
• Comparison of splittings used with the conjugate gradient algorithm
• Accuracy and effectiveness of preconditioned conjugate gradient algorithms for large and ill-conditioned problems
• Compatibility of approximate solution of linear equations with given error bounds for coefficients and right-hand sides
• An approach to nonlinear programming
• A robust incomplete Choleski-conjugate gradient algorithm
• Iterative Refinement Implies Numerical Stability for Gaussian Elimination
• Improving the efficiency of incomplete Choleski preconditionings
• Influence of the Eigenvalue Spectrum on the Convergence Rate of the Conjugate Gradient Method
• Iterative refinement implies numerical stability
• Solving Sparse Linear Systems with Sparse Backward Error

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