A block QMR algorithm for non-Hermitian linear systems with multiple right-hand sides

DOI10.1016/S0024-3795(96)00529-0zbMath0873.65021MaRDI QIDQ677905

Manish Malhotra, Roland W. Freund

Publication date: 16 April 1997

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

zbMATH Keywords

numerical experimentsdeflationKrylov subspace methodnon-Hermitian linear systemsLanczos processmultiple right hand sidesblock QMR methodquasi minimal residual property

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10)

Related Items

A breakdown-free block conjugate gradient method, On global randomized block Kaczmarz method for image reconstruction, A Seed Method for Solving Nonsymmetric Linear Systems with Multiple Right-hand Sides, Global GPBiCG method for complex non-Hermitian linear systems with multiple right-hand sides, The block Lanczos method for linear systems with multiple right-hand sides, Skew-symmetric methods for nonsymmetric linear systems with multiple right-hand sides, Block Variants of the COCG and COCR Methods for Solving Complex Symmetric Linear Systems with Multiple Right-Hand Sides, Global SCD algorithm for real positive definite linear systems with multiple right-hand sides, Incremental spectral preconditioners for sequences of linear systems, Exact and inexact breakdowns in the block GMRES method, Iterative solution of multiple radiation and scattering problems in structural acoustics using a block quasi-minimal residual algorithm, Block GPBi-CG method for solving nonsymmetric linear systems with multiple right-hand sides and its convergence analysis, Bi-CGSTAB as an induced dimension reduction method, Direct global Lanczos method for large linear systems with multiple right-hand sides, The method of difference potentials for the Helmholtz equation using compact high order schemes, Deflated and augmented global Krylov subspace methods for the matrix equations, A block preconditioner for the Gl-LSMR algorithm, An enhancement of the convergence of the IDR method, A second-order ensemble method based on a blended backward differentiation formula timestepping scheme for time-dependent Navier-Stokes equations, Admissible and Attainable Convergence Behavior of Block Arnoldi and GMRES, An Ensemble-Proper Orthogonal Decomposition Method for the Nonstationary Navier--Stokes Equations, Weighted and flexible versions of block CMRH method for solving nonsymmetric linear systems with multiple right-hand sides, A Krylov subspace projection method for simultaneous solution of Helmholtz problems at multiple frequencies., MINRES seed projection methods for solving symmetric linear systems with multiple right-hand sides, Block Krylov subspace methods for the computation of structural response to turbulent wind, On the block GMRES method with deflated restarting, A new family of global methods for linear systems with multiple right-hand sides, Updating the QR decomposition of block tridiagonal and block Hessenberg matrices, On the convergence of the Bl-LSQR algorithm for solving matrix equations, A deflated conjugate gradient method for multiple right hand sides and multiple shifts, A higher order ensemble simulation algorithm for fluid flows, The block Hessenberg process for matrix equations, Block conjugate gradient algorithms for least squares problems, The block CMRH method for solving nonsymmetric linear systems with multiple right-hand sides, Deflated GMRES for systems with multiple shifts and multiple right-hand sides, On Padé-type model order reduction of \(J\)-Hermitian linear dynamical systems, Indefinite Ruhe's variant of the block Lanczos method for solving the systems of linear equations, Unnamed Item, A block \(\mathrm{GCROT}(m, k)\) method for linear systems with multiple right-hand sides, Backward error analysis of the AllReduce algorithm for Householder QR decomposition, Computation of matrix-valued formally orthogonal polynomials and applications, A flexible and adaptive simpler block GMRES with deflated restarting for linear systems with multiple right-hand sides, A block IDR\((s)\) method for nonsymmetric linear systems with multiple right-hand sides, Block conjugate gradient type methods for the approximation of bilinear form \(C^HA^{-1}B\), Restarted block-GMRES with deflation of eigenvalues, Condition numbers for linear systems and Kronecker product linear systems with multiple right-hand sides, Efficient iterative algorithms for the stochastic finite element method with application to acoustic scattering, The block least squares method for solving nonsymmetric linear systems with multiple right-hand sides, Generalized global conjugate gradient squared algorithm, Convergence properties of some block Krylov subspace methods for multiple linear systems, Global least squares method (Gl-LSQR) for solving general linear systems with several right-hand sides, On short recurrence Krylov type methods for linear systems with many right-hand sides, A new deflated block GCROT(\(m,k\)) method for the solution of linear systems with multiple right-hand sides, A parallel generalized global conjugate gradient squared algorithm for linear systems with multiple right-hand sides, Development of the block BiCGGR2 method for linear systems with multiple right-hand sides, Efficient iterative solution of the three-dimensional Helmholtz equation, The simpler block CMRH method for linear systems, Improved seed methods for symmetric positive definite linear equations with multiple right‐hand sides, Extending the eigCG algorithm to nonsymmetric Lanczos for linear systems with multiple right-hand sides, Smoothing iterative block methods for linear systems with multiple right-hand sides, Numerical analysis of two ensemble eddy viscosity numerical regularizations of fluid motion, A block GMRES method augmented with eigenvectors, A Lanczos-type method for multiple starting vectors, Matrix Krylov subspace methods for linear systems with multiple right-hand sides, A novel class of block methods based on the blockAA^T-Lanczos bi-orthogonalization process for matrix equations, A block MINRES algorithm based on the band Lanczos method, Global LSMR(Gl-LSMR) method for solving general linear systems with several right-hand sides

Uses Software

• QMRPACK

Cites Work

• Unnamed Item
• Unnamed Item
• A survey of preconditioned iterative methods for linear systems of algebraic equations
• Exact non-reflecting boundary conditions
• The block conjugate gradient algorithm and related methods
• QMR: A quasi-minimal residual method for non-Hermitian linear systems
• Software for simplified Lanczos and QMR algorithms
• Implementation Aspects of Band Lanczos Algorithms for Computation of Eigenvalues of Large Sparse Symmetric Matrices
• Efficient Implementation of a Class of Preconditioned Conjugate Gradient Methods
• Conjugate Gradient-Type Methods for Linear Systems with Complex Symmetric Coefficient Matrices
• An Implementation of the QMR Method Based on Coupled Two-Term Recurrences
• A MATRIX-FREE INTERPRETATION OF THE NON-LOCAL DIRICHLET-TO-NEUMANN RADIATION BOUNDARY CONDITION
• Deflated and Augmented Krylov Subspace Techniques
• 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
• A Block QMR Method for Computing Multiple Simultaneous Solutions to Complex Symmetric Systems
• An Implementation of the Look-Ahead Lanczos Algorithm for Non-Hermitian Matrices
• The principle of minimized iterations in the solution of the matrix eigenvalue problem
• Methods of conjugate gradients for solving linear systems