Compact Two-Sided Krylov Methods for Nonlinear Eigenvalue Problems

DOI10.1137/17M1144167zbMath1397.65056OpenAlexW2750780521WikidataQ129283415 ScholiaQ129283415MaRDI QIDQ4683929

Pieter Lietaert, Françoise Tisseur, Karl Meerbergen

Publication date: 26 September 2018

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

Full work available at URL: https://doi.org/10.1137/17m1144167

zbMATH Keywords

nonlinear eigenvalue problemrational Krylovnonlinear eigensolvertwo-sided Krylov method

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Eigenvalues, singular values, and eigenvectors (15A18) Approximation by rational functions (41A20) Nonlinear spectral theory, nonlinear eigenvalue problems (47J10) Orthogonalization in numerical linear algebra (65F25) Matrix pencils (15A22)

Related Items

Block minimal bases \(\ell\)-ifications of matrix polynomials, Derivative Interpolating Subspace Frameworks for Nonlinear Eigenvalue Problems, The infinite Lanczos method for symmetric nonlinear eigenvalue problems, A simplified approach to Fiedler-like pencils via block minimal bases pencils

Uses Software

• NLEVP
• ABLE
• NLEIGS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A linear eigenvalue algorithm for the nonlinear eigenvalue problem
• A framework for analyzing nonlinear eigenproblems and parametrized linear systems
• Chebyshev interpolation for nonlinear eigenvalue problems
• Rational Krylov sequence methods for eigenvalue computation
• Nonlinear Rayleigh-Ritz iterative method for solving large scale nonlinear eigenvalue problems
• Nested Lanczos: Implicitly restarting an unsymmetric Lanczos algorithm
• The implicit application of a rational filter in the RKS method
• Backward error and condition of polynomial eigenvalue problems
• Stability Analysis of the Two-level Orthogonal Arnoldi Procedure
• Implicitly restarted Arnoldi with purification for the shift-invert transformation
• NLEVP
• Minimal Bases of Rational Vector Spaces, with Applications to Multivariable Linear Systems
• Linearization of matrix polynomials expressed in polynomial bases
• Large-Scale Optimization of Eigenvalues
• Reorthogonalization and Stable Algorithms for Updating the Gram-Schmidt QR Factorization
• The nonlinear eigenvalue problem
• A new family of companion forms of polynomial matrices
• ABLE: An Adaptive Block Lanczos Method for Non-Hermitian Eigenvalue Problems
• On Eigenvalue Optimization
• A Rational Krylov Method Based on Hermite Interpolation for Nonlinear Eigenvalue Problems
• NLEIGS: A Class of Fully Rational Krylov Methods for Nonlinear Eigenvalue Problems
• Linearization of Lagrange and Hermite interpolating matrix polynomials
• Compact Rational Krylov Methods for Nonlinear Eigenvalue Problems
• Matrix Polynomials
• A Framework for Structured Linearizations of Matrix Polynomials in Various Bases
• Krylov--Schur-Type Restarts for the Two-Sided Arnoldi Method
• Constructing Strong Linearizations of Matrix Polynomials Expressed in Chebyshev Bases
• The Infinite Bi-Lanczos Method for Nonlinear Eigenvalue Problems