Interpreting IDR as a Petrov–Galerkin Method

DOI10.1137/090774756zbMath1219.65039OpenAlexW2024363833WikidataQ115156440 ScholiaQ115156440MaRDI QIDQ2998014

Daniel B. Szyld, Valeria Simoncini

Publication date: 17 May 2011

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/090774756

zbMATH Keywords

iterative methodsKrylov subspace methodsnonsymmetric matrices

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Iterative numerical methods for linear systems (65F10) Linear equations (linear algebraic aspects) (15A06)

Related Items (14)

Minimizing synchronization in IDR (s ) ⋮ Recycling Krylov subspaces for CFD applications and a new hybrid recycling solver ⋮ The Induced Dimension Reduction Method Applied to Convection-Diffusion-Reaction Problems ⋮ Iterative processes in the Krylov-Sonneveld subspaces ⋮ IDR: a new generation of Krylov subspace methods? ⋮ Flexible and multi-shift induced dimension reduction algorithms for solving large sparse linear systems ⋮ IDR(\(s\)) for solving shifted nonsymmetric linear systems ⋮ An enhancement of the convergence of the IDR method ⋮ A variant of the IDR\((s)\) method with the quasi-minimal residual strategy ⋮ Krylov subspace recycling for sequences of shifted linear systems ⋮ Mstab: Stabilized Induced Dimension Reduction for Krylov Subspace Recycling ⋮ Two new efficient iterative regularization methods for image restoration problems ⋮ Accelerating the induced dimension reduction method using spectral information ⋮ Improvement of preconditioned bi-Lanczos-type algorithms with residual norm minimization for the stable solution of systems of linear equations

Uses Software

• JDQR
• BiCGstab
• mctoolbox
• JDQZ

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