A new family of global methods for linear systems with multiple right-hand sides

Authors:
Jianhua Zhang;Hua Dai;Jing Zhao
Affiliations:
Department of Mathematics, Anhui Science and Technology University, Fengyang 233100, China;Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China;Department of Mathematics, Anhui Science and Technology University, Fengyang 233100, China
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

Citing 16
Cited 0

Variants of BICGSTAB for matrices with complex spectrum

SIAM Journal on Scientific Computing
An iterative method for nonsymmetric systems with multiple right-hand sides

SIAM Journal on Scientific Computing
Variable Block CG Algorithms for Solving Large Sparse Symmetric Positive Definite Linear Systems on Parallel Computers, I: General Iterative Scheme

SIAM Journal on Matrix Analysis and Applications
A Stabilized QMR Version of Block BiCG

SIAM Journal on Matrix Analysis and Applications
Analysis of Projection Methods for Solving Linear Systems with Multiple Right-Hand Sides

SIAM Journal on Scientific Computing
Global FOM and GMRES algorithms for matrix equations

Applied Numerical Mathematics
A block GMRES method augmented with eigenvectors

Applied Mathematics and Computation
The block Lanczos method for linear systems with multiple right-hand sides

Applied Numerical Mathematics
Cache Issues of Algebraic Multigrid Methods for Linear Systems with Multiple Right-Hand Sides

SIAM Journal on Scientific Computing
A COCR method for solving complex symmetric linear systems

Journal of Computational and Applied Mathematics - Special issue: Scientific computing, computer arithmetic, and validated numerics (SCAN 2004)
A Hybrid Approach Combining Chebyshev Filter and Conjugate Gradient for Solving Linear Systems with Multiple Right-Hand Sides

SIAM Journal on Matrix Analysis and Applications
New convergence results on the global GMRES method for diagonalizable matrices

Journal of Computational and Applied Mathematics
An extension of the conjugate residual method to nonsymmetric linear systems

Journal of Computational and Applied Mathematics
Lanczos-type variants of the COCR method for complex nonsymmetric linear systems

Journal of Computational Physics
Restarted block-GMRES with deflation of eigenvalues

Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing
BiCR variants of the hybrid BiCG methods for solving linear systems with nonsymmetric matrices

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	7.29

Visualization

Abstract

The global bi-conjugate gradient (Gl-BCG) method is an attractive matrix Krylov subspace method for solving nonsymmetric linear systems with multiple right-hand sides, but it often show irregular convergence behavior in many applications. In this paper, we present a new family of global A-biorthogonal methods by using short two-term recurrences and formal orthogonal polynomials, which contain the global bi-conjugate residual (Gl-BCR) algorithm and its improved version. Finally, numerical experiments illustrate that the proposed methods are highly competitive and often superior to originals.