The block grade of a block Krylov space

DOI10.1016/j.laa.2008.07.008zbMath1163.65015OpenAlexW1993296015MaRDI QIDQ958009

Thomas Schmelzer, Martin H. Gutknecht

Publication date: 2 December 2008

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2008.07.008

zbMATH Keywords

gradeKrylov subspace methodsminimal polynomialblock Krylov subspace methodsmultiple right-hand sidesblock gradeblock size reductionnonsingular sparse linear systems

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Iterative numerical methods for linear systems (65F10)

Related Items (18)

A breakdown-free block conjugate gradient method ⋮ GPMR: An Iterative Method for Unsymmetric Partitioned Linear Systems ⋮ On multivariable proper rational interpolation using coprime factors ⋮ Sparse variational Bayesian approximations for nonlinear inverse problems: applications in nonlinear elastography ⋮ An enhancement of the convergence of the IDR method ⋮ Adaptively restarted block Krylov subspace methods with low-synchronization skeletons ⋮ A shifted block FOM algorithm with deflated restarting for matrix exponential computations ⋮ A posteriori superlinear convergence bounds for block conjugate gradient ⋮ The Block Rational Arnoldi Method ⋮ GMRES algorithms over 35 years ⋮ Block conjugate gradient algorithms for least squares problems ⋮ Deflated block Krylov subspace methods for large scale eigenvalue problems ⋮ Block minimum perturbation algorithm based on block Arnoldi process for nonsymmetric linear systems with multiple right-hand sides ⋮ A block IDR\((s)\) method for nonsymmetric linear systems with multiple right-hand sides ⋮ Block conjugate gradient type methods for the approximation of bilinear form \(C^HA^{-1}B\) ⋮ Development of the block BiCGGR2 method for linear systems with multiple right-hand sides ⋮ The simpler block CMRH method for linear systems ⋮ A block MINRES algorithm based on the band Lanczos method

Uses Software

• JDQR
• JDQZ
• ABLE

Cites Work

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• Implementation Aspects of Band Lanczos Algorithms for Computation of Eigenvalues of Large Sparse Symmetric Matrices
• A Completed Theory of the Unsymmetric Lanczos Process and Related Algorithms, Part I
• A Completed Theory of the Unsymmetric Lanczos Process and Related Algorithms. Part II
• A Lanczos-type method for multiple starting vectors
• A Note on Preconditioning for Indefinite Linear Systems
• Templates for the Solution of Algebraic Eigenvalue Problems
• Advanced Linear Algebra
• ABLE: An Adaptive Block Lanczos Method for Non-Hermitian Eigenvalue Problems
• Any Nonincreasing Convergence Curve is Possible for GMRES
• Methods of conjugate gradients for solving linear systems

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