Clusters, preconditioners, convergence

DOI10.1016/S0024-3795(96)00445-4zbMath0917.65032MaRDI QIDQ1368758

A. Yu. Yeremin, Nikolai L. Zamarashkin, Evgenij E. Tyrtyshnikov

Publication date: 29 September 1997

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

zbMATH Keywords

convergenceGMRESclusters of eigenvaluesToeplitz matricesgeneralized minimal residual methodcirculant preconditionersclusters of singular values

Mathematics Subject Classification ID

Inequalities involving eigenvalues and eigenvectors (15A42) Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35)

Related Items (11)

Absolute equal distribution of families of finite sets. ⋮ Absolute equal distribution of the spectra of Hermitian matrices ⋮ Preconditioning for Nonsymmetry and Time-Dependence ⋮ A unifying approach to the construction of circulant preconditioners ⋮ Optimal rank matrix algebras preconditioners ⋮ Preconditioners for image restoration by reblurring techniques ⋮ A preconditioning approach to the pagerank computation problem ⋮ A classification scheme for regularizing preconditioners, with application to Toeplitz systems ⋮ Optimal trigonometric preconditioners for nonsymmetric Toeplitz systems ⋮ On uniform connectivity of algebraic matrix sets ⋮ A Preconditioned MINRES Method for Nonsymmetric Toeplitz Matrices

Cites Work

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• On the rate of convergence of the preconditioned conjugate gradient method
• Circulant preconditioners with unbounded inverses
• A unifying approach to some old and new theorems on distribution and clustering
• An Optimal Circulant Preconditioner for Toeplitz Systems
• Toeplitz Equations by Conjugate Gradients with Circulant Preconditioner
• Parallel Preconditioning with Sparse Approximate Inverses
• Which circulant preconditioner is better?

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