IDR: a new generation of Krylov subspace methods?
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Publication:389573
DOI10.1016/j.laa.2012.11.021zbMath1305.65118OpenAlexW2098892412MaRDI QIDQ389573
Olaf Rendel, Anisa Rizvanolli, Jens-Peter M. Zemke
Publication date: 21 January 2014
Published in: Linear Algebra and its Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.laa.2012.11.021
linear systemiterative methodKrylov subspace methodinduced dimension reductioneigenvalue computationtranspose-free method
Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Iterative numerical methods for linear systems (65F10)
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A quasi-minimal residual variant of IDRstab using the residual smoothing technique ⋮ Iterative processes in the Krylov-Sonneveld subspaces ⋮ Flexible and multi-shift induced dimension reduction algorithms for solving large sparse linear systems ⋮ A variant of IDRstab with reliable update strategies for solving sparse linear systems
Uses Software
Cites Work
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- Bi-CGSTAB as an induced dimension reduction method
- GBi-CGSTAB(\(s,L\)): IDR(\(s\)) with higher-order stabilization polynomials
- IDR explained
- Transpose-free formulations of Lanczos-type methods for nonsymmetric linear systems
- A composite step conjugate gradients squared algorithm for solving nonsymmetric linear systems
- BiCGstab(\(l\)) for linear equations involving unsymmetric matrices with complex spectrum
- Maintaining convergence properties of BiCGStab methods in finite precision arithmetic
- Generalized conjugate gradient squared
- Quasi-minimal residual smoothing technique for the IDR($s$) method
- An alternative implementation of the IDRstab method saving vector updates
- Eigenvalue Computations Based on IDR
- Algorithm 913
- Interpreting IDR as a Petrov–Galerkin Method
- Exploiting BiCGstab($\ell$) Strategies to Induce Dimension Reduction
- IDR(s): A Family of Simple and Fast Algorithms for Solving Large Nonsymmetric Systems of Linear Equations
- CGS, A Fast Lanczos-Type Solver for Nonsymmetric Linear systems
- Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
- Variants of BICGSTAB for Matrices with Complex Spectrum
- A Quasi-Minimal Residual Variant of the Bi-CGSTAB Algorithm for Nonsymmetric Systems
- GPBi-CG: Generalized Product-type Methods Based on Bi-CG for Solving Nonsymmetric Linear Systems
- A Lanczos-type method for multiple starting vectors
- ML(k)BiCGSTAB: A BiCGSTAB Variant Based on Multiple Lanczos Starting Vectors
- Composite Step Product Methods for Solving Nonsymmetric Linear Systems
- Relations between Galerkin and Norm-Minimizing Iterative Methods for Solving Linear Systems
- On the Convergence Behavior of IDR($s$) and Related Methods
- A Transpose-Free Quasi-Minimal Residual Algorithm for Non-Hermitian Linear Systems
- The principle of minimized iterations in the solution of the matrix eigenvalue problem
- Methods of conjugate gradients for solving linear systems
