Parallel Krylov Solvers for the Polynomial Eigenvalue Problem in SLEPc
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Publication:2830622
DOI10.1137/15M1022458zbMath1352.65116OpenAlexW2539553730MaRDI QIDQ2830622
Publication date: 28 October 2016
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/15m1022458
eigenvaluesnumerical experimentsparallel computingprojection methodsmatrix polynomialKrylov subspacespectral transformationSLEPccompanion linearizationnonmonomial bases
Computational methods for sparse matrices (65F50) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Parallel numerical computation (65Y05) Matrices over function rings in one or more variables (15A54)
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Uses Software
Cites Work
- Unnamed Item
- A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling
- Perturbation, extraction and refinement of invariant pairs for matrix polynomials
- Chebyshev interpolation for nonlinear eigenvalue problems
- A block Newton method for nonlinear eigenvalue problems
- A parallel additive Schwarz preconditioned Jacobi-Davidson algorithm for polynomial eigenvalue problems in quantum dot simulation
- Block \(\mathbf {LU}\) factors of generalized companion matrix pencils
- Backward error and condition of polynomial eigenvalue problems
- The Quadratic Eigenvalue Problem
- A Krylov--Schur Algorithm for Large Eigenproblems
- Parallel iterative refinement in polynomial eigenvalue problems
- NLEVP
- An algorithm for the complete solution of quadratic eigenvalue problems
- SLEPc
- Backward Error of Polynomial Eigenproblems Solved by Linearization
- Linearization of matrix polynomials expressed in polynomial bases
- Optimal Scaling of Generalized and Polynomial Eigenvalue Problems
- The Quadratic Arnoldi Method for the Solution of the Quadratic Eigenvalue Problem
- Templates for the Solution of Algebraic Eigenvalue Problems
- Normwise Scaling of Second Order Polynomial Matrices
- A Multilevel Jacobi–Davidson Method for Polynomial PDE Eigenvalue Problems Arising in Plasma Physics
- SOAR: A Second-order Arnoldi Method for the Solution of the Quadratic Eigenvalue Problem
- Vector Spaces of Linearizations for Matrix Polynomials
- Memory-efficient Arnoldi algorithms for linearizations of matrix polynomials in Chebyshev basis