SPMR: A Family of Saddle-Point Minimum Residual Solvers

DOI10.1137/16M1102410zbMath1448.65022OpenAlexW2809990467MaRDI QIDQ4569320

Ron Estrin, Chen Greif

Publication date: 28 June 2018

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/16m1102410

zbMATH Keywords

preconditioningKrylov subspace methodsiterative solversaddle-point systemminimum residual methods

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Eigenvalues, singular values, and eigenvectors (15A18) Iterative numerical methods for linear systems (65F10) Linear equations (linear algebraic aspects) (15A06) Orthogonalization in numerical linear algebra (65F25) Preconditioners for iterative methods (65F08)

Related Items (4)

GPMR: An Iterative Method for Unsymmetric Partitioned Linear Systems ⋮ Iterative solution of saddle-point systems of linear equations ⋮ Implementing a Smooth Exact Penalty Function for General Constrained Nonlinear Optimization ⋮ Iterative preconditioned methods in Krylov spaces: trends of the 21st century

Uses Software

• LSQR
• Eigtool
• LSMR
• CRAIG

Cites Work

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• Computing projections with LSQR
• Approximating the leading singular triplets of a large matrix function
• QMR: A quasi-minimal residual method for non-Hermitian linear systems
• On the Solution of Equality Constrained Quadratic Programming Problems Arising in Optimization
• A Backward Error Analysis of a Null Space Algorithm in Sparse Quadratic Programming
• Generalized Golub--Kahan Bidiagonalization and Stopping Criteria
• Finite Elements and Fast Iterative Solvers
• Towards an optimal condition number of certain augmented Lagrangian-type saddle-point matrices
• Range-Space Variants and Inexact Matrix-Vector Products in Krylov Solvers for Linear Systems Arising from Inverse Problems
• LSMR: An Iterative Algorithm for Sparse Least-Squares Problems
• Preconditioners for the discretized time-harmonic Maxwell equations in mixed form
• Numerical solution of saddle point problems
• A Look-Ahead Lanczos Algorithm for Unsymmetric Matrices
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Two Conjugate-Gradient-Type Methods for Unsymmetric Linear Equations
• LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
• Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
• Theory of Inexact Krylov Subspace Methods and Applications to Scientific Computing
• Constraint Preconditioning for Indefinite Linear Systems
• Inexact Krylov Subspace Methods for Linear Systems
• Any Nonincreasing Convergence Curve is Possible for GMRES
• The Use ofQRFactorization in Sparse Quadratic Programming and Backward Error Issues
• Bounds on Eigenvalues of Matrices Arising from Interior-Point Methods
• Projected Krylov Methods for Saddle-Point Systems
• Preconditioning
• On Nonsingular Saddle-Point Systems with a Maximally Rank Deficient Leading Block
• An Implementation of the Look-Ahead Lanczos Algorithm for Non-Hermitian Matrices
• Calculating the Singular Values and Pseudo-Inverse of a Matrix

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