Weighted Inner Products for GMRES and GMRES-DR

DOI10.1137/16M1082615zbMath1392.65051arXiv1607.00255MaRDI QIDQ5372646

Mark Embree, Huy V. Nguyen, Ronald B. Morgan

Publication date: 27 October 2017

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

Full work available at URL: https://arxiv.org/abs/1607.00255

zbMATH Keywords

deflationlinear equationsrestarted GMRESweighted inner productlocalized eigenvectorsGMRES-DRW-GMRES-DCT

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10) Linear equations (linear algebraic aspects) (15A06)

Related Items (3)

Limited‐memory polynomial methods for large‐scale matrix functions ⋮ GMRES algorithms over 35 years ⋮ Weighted and deflated global GMRES algorithms for solving large Sylvester matrix equations

Uses Software

• MatrixMarket
• Eigtool

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Some observations on weighted GMRES
• Numerical stability of orthogonalization methods with a non-standard inner product
• A new computational GMRES method
• Minimum residual methods for augmented systems
• Weighted FOM and GMRES for solving nonsymmetric linear systems
• The superlinear convergence behaviour of GMRES
• A note on weighted FOM and GMRES for solving nonsymmetric linear systems
• Restarted GMRES preconditioned by deflation
• A simple strategy for varying the restart parameter in GMRES\((m)\)
• Spectral deflation in Krylov solvers: a theory of coordinate space based methods
• On the choice of preconditioner for minimum residual methods for non-Hermitian matrices
• On nonsymmetric saddle point matrices that allow conjugate gradient iterations
• Weighted restarting method in the weighted Arnoldi algorithm for computing the eigenvalues of a nonsymmetric matrix
• On the Construction of Deflation-Based Preconditioners
• Deflated and Restarted Symmetric Lanczos Methods for Eigenvalues and Linear Equations with Multiple Right-Hand Sides
• Restarting the Nonsymmetric Lanczos Algorithm for Eigenvalues and Linear Equations Including Multiple Right-Hand Sides
• Necessary and Sufficient Conditions for the Existence of a Conjugate Gradient Method
• Complementary cycles of restarted GMRES
• Recycling Krylov Subspaces for Sequences of Linear Systems
• Combination Preconditioning and the Bramble–Pasciak$^{+}$ Preconditioner
• The Faber–Manteuffel Theorem for Linear Operators
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• A Preconditioning Technique for Indefinite Systems Resulting from Mixed Approximations of Elliptic Problems
• Adaptively Preconditioned GMRES Algorithms
• Truncation Strategies for Optimal Krylov Subspace Methods
• The Discrete Cosine Transform
• Analysis of Augmented Krylov Subspace Methods
• Deflated and Augmented Krylov Subspace Techniques
• Block-Triangular Preconditioners for Saddle Point Problems with a Penalty Term
• The Tortoise and the Hare Restart GMRES
• Convergence of Restarted Krylov Subspaces to Invariant Subspaces
• Minimal Residual Method Stronger than Polynomial Preconditioning
• GMRES with Deflated Restarting
• Eigenvalue translation based preconditioners for the GMRES(k) method
• A Restarted GMRES Method Augmented with Eigenvectors
• GMRESR: a family of nested GMRES methods
• On the convergence behavior of the restarted GMRES algorithm for solving nonsymmetric linear systems
• A Flexible Inner-Outer Preconditioned GMRES Algorithm
• A Technique for Accelerating the Convergence of Restarted GMRES
• Modified Gram-Schmidt (MGS), Least Squares, and Backward Stability of MGS-GMRES
• Accelerate weighted GMRES by augmenting error approximations

This page was built for publication: Weighted Inner Products for GMRES and GMRES-DR