A block IDR\((s)\) method for nonsymmetric linear systems with multiple right-hand sides

DOI10.1016/j.cam.2011.02.035zbMath1219.65037OpenAlexW1994115828MaRDI QIDQ548308

Bo Yu, Yusaku Yamamoto, Tomohiro Sogabe, Shao-Liang Zhang, Lei Du

Publication date: 28 June 2011

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.2011.02.035

zbMATH Keywords

algorithmsnumerical experimentsblock methodBiCGStabmultiple right-hand sidesinduced dimension reductionBi-CG based methodslarge nonsymmetric linear systems

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10)

Related Items (14)

An accurate and efficient acoustic eigensolver based on a fast multipole BEM and a contour integral method ⋮ Block Variants of the COCG and COCR Methods for Solving Complex Symmetric Linear Systems with Multiple Right-Hand Sides ⋮ A Block Preconditioned Harmonic Projection Method for Large-Scale Nonlinear Eigenvalue Problems ⋮ IDR(\(s\)) for solving shifted nonsymmetric linear systems ⋮ Kω -- open-source library for the shifted Krylov subspace method of the form \((z I - H)x = b\) ⋮ The Block Rational Arnoldi Method ⋮ Accelerating data uncertainty quantification by solving linear systems with multiple right-hand sides ⋮ MINRES seed projection methods for solving symmetric linear systems with multiple right-hand sides ⋮ A variant of the IDR\((s)\) method with the quasi-minimal residual strategy ⋮ The block CMRH method for solving nonsymmetric linear systems with multiple right-hand sides ⋮ A block \(\mathrm{GCROT}(m, k)\) method for linear systems with multiple right-hand sides ⋮ ML(\(n\))BiCGStabt: a ML(\(n\))BiCGStab variant with \(\mathbf A\)-transpose ⋮ Block conjugate gradient type methods for the approximation of bilinear form \(C^HA^{-1}B\) ⋮ A new deflated block GCROT(\(m,k\)) method for the solution of linear systems with multiple right-hand sides

Uses Software

• SparseMatrix

Cites Work

• Unnamed Item
• Bi-CGSTAB as an induced dimension reduction method
• A block QMR algorithm for non-Hermitian linear systems with multiple right-hand sides
• GBi-CGSTAB(\(s,L\)): IDR(\(s\)) with higher-order stabilization polynomials
• Simpler block GMRES for nonsymmetric systems with multiple right-hand sides
• Oblique projection methods for linear systems with multiple right-hand sides
• The block grade of a block Krylov space
• The block conjugate gradient algorithm and related methods
• BiCGstab(\(l\)) for linear equations involving unsymmetric matrices with complex spectrum
• Transpose-free multiple Lanczos and its application in Padé approximation
• A block version of BiCGSTAB for linear systems with multiple right-hand sides
• Global FOM and GMRES algorithms for matrix equations
• The block Lanczos method for linear systems with multiple right-hand sides
• Skew-symmetric methods for nonsymmetric linear systems with multiple right-hand sides
• The block least squares method for solving nonsymmetric linear systems with multiple right-hand sides
• Convergence properties of block GMRES and matrix polynomials
• Matrix Krylov subspace methods for linear systems with multiple right-hand sides
• QMR-Based Projection Techniques for the Solution of Non-Hermitian Systems with Multiple Right-Hand Sides
• Algorithm 913
• 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
• Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
• Numerical Linear Algebra for High-Performance Computers
• A Stabilized QMR Version of Block BiCG
• Analysis of Projection Methods for Solving Linear Systems with Multiple Right-Hand Sides
• ML(k)BiCGSTAB: A BiCGSTAB Variant Based on Multiple Lanczos Starting Vectors
• An Iterative Method for Nonsymmetric Systems with Multiple Right-Hand Sides
• Variable Block CG Algorithms for Solving Large Sparse Symmetric Positive Definite Linear Systems on Parallel Computers, I: General Iterative Scheme
• Improved seed methods for symmetric positive definite linear equations with multiple right‐hand sides
• The global Hessenberg and CMRH methods for linear systems with multiple right-hand sides

This page was built for publication: A block IDR\((s)\) method for nonsymmetric linear systems with multiple right-hand sides