A breakdown of the block CG method

DOI10.1080/10556789608805643zbMath0933.65037OpenAlexW2037836444MaRDI QIDQ4354080

Charles Broyden

Publication date: 20 March 2000

Published in: Optimization Methods and Software (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10556789608805643

zbMATH Keywords

comparison of methodsstability analysisLanczos methodbreakdownHestenes-Stiefel methodblock conjugate gradient methodindefinite symmetric or nonsymmetric systems

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35) Conditioning of matrices (15A12)

Related Items (3)

A breakdown-free block conjugate gradient method ⋮ Enhancing Block Cimmino for Sparse Linear Systems with Dense Columns via Schur Complement ⋮ A review of formal orthogonality in Lanczos-based methods

Cites Work

• Generating conjugate directions for arbitrary matrices by matrix equations. I
• A breakdown-free Lanczos type algorithm for solving linear systems
• The block conjugate gradient algorithm and related methods
• QMR: A quasi-minimal residual method for non-Hermitian linear systems
• Avoiding breakdown and near-breakdown in Lanczos type algorithms
• A conjugate direction algorithm without line searches
• Matrix Analysis
• LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
• A Completed Theory of the Unsymmetric Lanczos Process and Related Algorithms, Part I
• Solution of Sparse Indefinite Systems of Linear Equations
• A Completed Theory of the Unsymmetric Lanczos Process and Related Algorithms. Part II
• Error Propagation in Numerical Processes
• Variable Block CG Algorithms for Solving Large Sparse Symmetric Positive Definite Linear Systems on Parallel Computers, I: General Iterative Scheme
• Hyperbolic Pairs in the Method of Conjugate Gradients

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