A novel class of block methods based on the blockAAT-Lanczos bi-orthogonalization process for matrix equations

DOI10.1080/00207160.2012.718072zbMath1278.65035OpenAlexW2073686283MaRDI QIDQ2868174

Zhang, Jianhua, Jing Zhao

Publication date: 23 December 2013

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160.2012.718072

zbMATH Keywords

multiple right-hand sidesnonsymmetric linear systemsblock Krylov subspace\(AA^T\)-LanczosBl-BCG

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Iterative numerical methods for linear systems (65F10) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

Related Items (2)

Block Variants of the COCG and COCR Methods for Solving Complex Symmetric Linear Systems with Multiple Right-Hand Sides ⋮ Improvement of the accuracy of the approximate solution of the Block BiCR method

Cites Work

• Restarted block-GMRES with deflation of eigenvalues
• A block QMR algorithm for non-Hermitian linear systems with multiple right-hand sides
• Lanczos-type variants of the COCR method for complex nonsymmetric linear systems
• Deflated GMRES for systems with multiple shifts and multiple right-hand sides
• BiCR variants of the hybrid BiCG methods for solving linear systems with nonsymmetric matrices
• Generalized global conjugate gradient squared algorithm
• An extension of the conjugate residual method to nonsymmetric linear systems
• The block conjugate gradient algorithm and related methods
• Smoothing iterative block methods for linear systems with multiple right-hand sides
• Iterative solution of multiple radiation and scattering problems in structural acoustics using a block quasi-minimal residual algorithm
• A block variant of the GMRES method on massively parallel processors
• Global FOM and GMRES algorithms for matrix equations
• A block GMRES method augmented with eigenvectors
• The block Lanczos method for linear systems with multiple right-hand sides
• Maintaining convergence properties of BiCGStab methods in finite precision arithmetic
• Global SCD algorithm for real positive definite linear systems with multiple right-hand sides
• CG-type algorithms to solve symmetric matrix equations
• The block least squares method for solving nonsymmetric linear systems with multiple right-hand sides
• Convergence properties of block GMRES and matrix polynomials
• Implicitly restarted global FOM and GMRES for nonsymmetric matrix equations and Sylvester equations
• Matrix Krylov subspace methods for linear systems with multiple right-hand sides
• Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
• Variants of BICGSTAB for Matrices with Complex Spectrum
• A Stabilized QMR Version of Block BiCG
• Analysis of Projection Methods for Solving Linear Systems with Multiple Right-Hand Sides
• ABLE: An Adaptive Block Lanczos Method for Non-Hermitian Eigenvalue Problems
• 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
• On the convergence of the Bl-LSQR algorithm for solving matrix equations
• The global Hessenberg and CMRH methods for linear systems with multiple right-hand sides

This page was built for publication: A novel class of block methods based on the blockAA^T-Lanczos bi-orthogonalization process for matrix equations