<scp>TriCG</scp> and <scp>TriMR</scp>: Two Iterative Methods for Symmetric Quasi-definite Systems

DOI10.1137/20M1363030MaRDI QIDQ5005013

Dominique Orban, Alexis Montoison

Publication date: 4 August 2021

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

Full work available at URL: https://arxiv.org/abs/2008.12863

zbMATH Keywords

iterative methodsinterior-point methodsKrylov subspacessaddle-point systemsBlock-Lanczos processorthogonal tridiagonalization processstabilized Stokes equationssymmetric quasi-definite systems

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Ill-posedness and regularization problems in numerical linear algebra (65F22) Large-scale problems in mathematical programming (90C06) Applications of mathematical programming (90C90) Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35) Orthogonalization in numerical linear algebra (65F25) Preconditioners for iterative methods (65F08)

Related Items

HyKKT: a hybrid direct-iterative method for solving KKT linear systems, GPMR: An Iterative Method for Unsymmetric Partitioned Linear Systems

Uses Software

• LSQR
• IFISS
• SparseMatrix
• MINRES-QLP
• LSMR
• MINRES
• Julia
• GitHub
• Krylov.jl
• CRAIG

Cites Work

• Approximation of the scattering amplitude and linear systems
• The block conjugate gradient algorithm and related methods
• A primal-dual regularized interior-point method for convex quadratic programs
• The block Lanczos method for linear systems with multiple right-hand sides
• Finite Elements and Fast Iterative Solvers
• Julia: A Fresh Approach to Numerical Computing
• Iterative Solution of Symmetric Quasi-Definite Linear Systems
• The university of Florida sparse matrix collection
• MINRES-QLP: A Krylov Subspace Method for Indefinite or Singular Symmetric Systems
• LSMR: An Iterative Algorithm for Sparse Least-Squares Problems
• LSLQ: An Iterative Method for Linear Least-Squares with an Error Minimization Property
• Two Conjugate-Gradient-Type Methods for Unsymmetric Linear Equations
• LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
• Solution of Sparse Indefinite Systems of Linear Equations
• Regularized symmetric indefinite systems in interior point methods for linear and quadratic optimization
• A Note on Preconditioning for Indefinite Linear Systems
• Symmetric Quasidefinite Matrices
• Mixed Finite Element Methods and Applications
• BiLQ: An Iterative Method for Nonsymmetric Linear Systems with a Quasi-Minimum Error Property
• LNLQ: An Iterative Method for Least-Norm Problems with an Error Minimization Property
• A Tridiagonalization Method for Symmetric Saddle-Point Systems
• Bidiagonalization of Matrices and Solution of Linear Equations
• Methods of conjugate gradients for solving linear systems
• The N‐Step Iteration Procedures
• Finite Elements
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