Restarted Hessenberg method for solving shifted nonsymmetric linear systems
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Publication:1678125
DOI10.1016/j.cam.2017.09.047zbMath1377.65042arXiv1507.08141OpenAlexW2549767625MaRDI QIDQ1678125
Xian-Ming Gu, Chun Wen, Lei Du, Ting-Zhu Huang, Bruno Carpentieri, Guojian Yin
Publication date: 14 November 2017
Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1507.08141
algorithmconvergence accelerationnumerical experimentfractional differential equationspivoting strategyHessenberg processfull orthogonalization methodcollinearrestarted Hessenberg methodshifted linear system
Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Iterative numerical methods for linear systems (65F10) Orthogonalization in numerical linear algebra (65F25) Fractional partial differential equations (35R11)
Related Items (18)
Heavy ball restarted CMRH methods for linear systems ⋮ A tensor format for the generalized Hessenberg method for solving Sylvester tensor equations ⋮ Augmented and deflated CMRH method for solving nonsymmetric linear systems ⋮ Preconditioners for Krylov subspace methods: An overview ⋮ A shifted block FOM algorithm with deflated restarting for matrix exponential computations ⋮ A flexible and adaptive simpler GMRES with deflated restarting for shifted linear systems ⋮ On global Hessenberg based methods for solving Sylvester matrix equations ⋮ Simultaneous band reduction of two symmetric matrices ⋮ Multipreconditioned GMRES for simulating stochastic automata networks ⋮ Unnamed Item ⋮ Extended and rational Hessenberg methods for the evaluation of matrix functions ⋮ On restarted and deflated block FOM and GMRES methods for sequences of shifted linear systems ⋮ A flexible global GCRO-DR method for shifted linear systems and general coupled matrix equations ⋮ Restarted simpler GMRES augmented with harmonic Ritz vectors and approximate errors ⋮ Efficient variants of the CMRH method for solving a sequence of multi-shifted non-Hermitian linear systems simultaneously ⋮ The simpler block CMRH method for linear systems ⋮ Preconditioned iterative methods for multi-linear systems based on the majorization matrix ⋮ A Hessenberg-type algorithm for computing PageRank problems
Uses Software
Cites Work
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- On the convergence of Q-OR and Q-MR Krylov methods for solving nonsymmetric linear systems
- Any finite convergence curve is possible in the initial iterations of restarted FOM
- IDR(\(s\)) for solving shifted nonsymmetric linear systems
- BiCGStab(\(\ell\)) for families of shifted linear systems
- A new look at CMRH and its relation to GMRES
- On the use of matrix functions for fractional partial differential equations
- An iterative method to compute the sign function of a non-Hermitian matrix and its application to the overlap Dirac operator at nonzero chemical potential
- Arnoldi methods for large Sylvester-like observer matrix equations, and an associated algorithm for partial spectrum assignment
- Deflated GMRES for systems with multiple shifts and multiple right-hand sides
- Restarted weighted full orthogonalization method for shifted linear systems
- On a variable smoothing procedure for Krylov subspace methods
- A projection method for generalized eigenvalue problems using numerical integration.
- Restarted full orthogonalization method for shifted linear systems
- Generalized product-type methods based on bi-conjugate gradient (GPBiCG) for solving shifted linear systems
- CMRH: A new method for solving nonsymmetric linear systems based on the Hessenberg reduction algorithm
- Iterative system solvers for the frequency analysis of linear mechanical systems
- BiCR-type methods for families of shifted linear systems
- Talbot quadratures and rational approximations
- Krylov subspace recycling for sequences of shifted linear systems
- A new implementation of the CMRH method for solving dense linear systems
- A flexible CMRH algorithm for nonsymmetric linear systems
- A Numerical Method for Calculating the Green's Function Arising from Electronic Structure Theory
- Flexible and multi-shift induced dimension reduction algorithms for solving large sparse linear systems
- The university of Florida sparse matrix collection
- Recycling BiCG with an Application to Model Reduction
- Nested Krylov Methods for Shifted Linear Systems
- Parabolic and hyperbolic contours for computing the Bromwich integral
- Restarted GMRES for Shifted Linear Systems
- Galerkin Projection Methods for Solving Multiple Linear Systems
- Accuracy and Stability of Numerical Algorithms
- A Restarted GMRES Method Augmented with Eigenvectors
- A Preconditioned and Shifted GMRES Algorithm for the PageRank Problem with Multiple Damping Factors
- Restarted Full Orthogonalization Method with Deflation for Shifted Linear Systems
- Preconditioned Multishift BiCG for $\mathcal{H}_2$-Optimal Model Reduction
- A Flexible Krylov Solver for Shifted Systems with Application to Oscillatory Hydraulic Tomography
- Restarted GMRES augmented with harmonic Ritz vectors for shifted linear systems
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