IDR(\(s\)) for solving shifted nonsymmetric linear systems

DOI10.1016/j.cam.2014.07.004zbMath1310.65037OpenAlexW2021146521MaRDI QIDQ399069

Tomohiro Sogabe, Lei Du, Shao-Liang Zhang

Publication date: 19 August 2014

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2014.07.004

zbMATH Keywords

Krylov subspaceinduced dimension reductionIDR(\(s\))shifted IDR(\(s\))shifted linear systems

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10)

Related Items

GMRES convergence bounds for eigenvalue problems, Nested Krylov Methods for Shifted Linear Systems, Restarted Hessenberg method for solving shifted nonsymmetric linear systems, Kω -- open-source library for the shifted Krylov subspace method of the form \((z I - H)x = b\), Preconditioned Chebyshev BiCG method for parameterized linear systems, A flexible and adaptive simpler GMRES with deflated restarting for shifted linear systems, Flexible and deflated variants of the block shifted GMRES method, Efficient variants of the CMRH method for solving a sequence of multi-shifted non-Hermitian linear systems simultaneously, Minimal residual-like condition with collinearity for shifted Krylov subspace methods

Uses Software

• SparseMatrix

Cites Work

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• BiCGStab(\(\ell\)) for families of shifted linear systems
• A block IDR\((s)\) method for nonsymmetric linear systems with multiple right-hand sides
• Bi-CGSTAB as an induced dimension reduction method
• A variant of the IDR\((s)\) method with the quasi-minimal residual strategy
• GBi-CGSTAB(\(s,L\)): IDR(\(s\)) with higher-order stabilization polynomials
• On a weighted quasi-residual minimization strategy for solving complex symmetric shifted linear systems
• IDR explained
• Restarted weighted full orthogonalization method for shifted linear systems
• BiCGstab(\(l\)) for linear equations involving unsymmetric matrices with complex spectrum
• Restarted full orthogonalization method for shifted linear systems
• Weighted restarting method in the weighted Arnoldi algorithm for computing the eigenvalues of a nonsymmetric matrix
• On the Convergence of Restarted Krylov Subspace Methods
• A Numerical Method for Calculating the Green's Function Arising from Electronic Structure Theory
• Quasi-minimal residual smoothing technique for the IDR($s$) method
• Eigenvalue Computations Based on IDR
• Minimizing synchronization in IDR (s )
• The university of Florida sparse matrix collection
• Interpreting IDR as a Petrov–Galerkin Method
• Exploiting BiCGstab($\ell$) Strategies to Induce Dimension Reduction
• IDR(s): A Family of Simple and Fast Algorithms for Solving Large Nonsymmetric Systems of Linear Equations
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
• Restarted GMRES for Shifted Linear Systems
• ML(k)BiCGSTAB: A BiCGSTAB Variant Based on Multiple Lanczos Starting Vectors
• An Extension of the COCR Method to Solving Shifted Linear Systems with Complex Symmetric Matrices
• Restarted GMRES augmented with harmonic Ritz vectors for shifted linear systems
• Methods of conjugate gradients for solving linear systems