CG-type algorithms to solve symmetric matrix equations

DOI10.1016/j.amc.2005.03.003zbMath1104.65029OpenAlexW2055000341MaRDI QIDQ2489397

Davod Khojasteh Salkuyeh

Publication date: 28 April 2006

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

Full work available at URL: https://doi.org/10.1016/j.amc.2005.03.003

zbMATH Keywords

numerical examplesmatrix equationsKrylov subspace methodmultiple right-hand sidessymmetric linear systemsconjugate gradient type algorithmsGlobal FOM GMRES algorithms

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10)

Related Items

A breakdown-free block conjugate gradient method ⋮ Global GPBiCG method for complex non-Hermitian linear systems with multiple right-hand sides ⋮ Nested splitting conjugate gradient method for matrix equation \(AXB=C\) and preconditioning ⋮ Global SCD algorithm for real positive definite linear systems with multiple right-hand sides ⋮ Unnamed Item ⋮ A new approximate inverse preconditioner based on the Vaidya’s maximum spanning tree for matrix equation AXB = C ⋮ Deflated and augmented global Krylov subspace methods for the matrix equations ⋮ A block preconditioner for the Gl-LSMR algorithm ⋮ A new family of global methods for linear systems with multiple right-hand sides ⋮ A global harmonic Arnoldi method for large non-Hermitian eigenproblems with an application to multiple eigenvalue problems ⋮ The right–left preconditioning technique for the solution of the large matrix equationAXB = C ⋮ Generalized global conjugate gradient squared algorithm ⋮ Unnamed Item ⋮ On the Krylov subspace methods based on tensor format for positive definite Sylvester tensor equations ⋮ The symmetric solutions of the matrix inequalityAX≥Bin least-squares sense ⋮ A novel class of block methods based on the blockAA^T-Lanczos bi-orthogonalization process for matrix equations ⋮ Global LSMR(Gl-LSMR) method for solving general linear systems with several right-hand sides

Uses Software

• Algorithm 432

Cites Work

• Unnamed Item
• The block conjugate gradient algorithm and related methods
• Global FOM and GMRES algorithms for matrix equations
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• A Hessenberg-Schur method for the problem AX + XB= C
• An Iterative Method for Nonsymmetric Systems with Multiple Right-Hand Sides
• Algorithm 432 [C2: Solution of the matrix equation AX + XB = C [F4]]
• Methods of conjugate gradients for solving linear systems