The Infinite Bi-Lanczos Method for Nonlinear Eigenvalue Problems

DOI10.1137/16M1084195zbMath1392.65093arXiv1607.03454MaRDI QIDQ5372659

Elias Jarlebring, Sarah W. Gaaf

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/1607.03454

zbMATH Keywords

nonlinear eigenvalue problemtwo-sided Lanczos methodinfinite bi-Lanczos methodinfinite two-sided Lanczos method

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Numerical solution of nonlinear eigenvalue and eigenvector problems (65H17)

Related Items (7)

A Block Preconditioned Harmonic Projection Method for Large-Scale Nonlinear Eigenvalue Problems ⋮ On Krylov complexity in open systems: an approach via bi-Lanczos algorithm ⋮ Rational Krylov and ADI iteration for infinite size quasi-Toeplitz matrix equations ⋮ Operator dynamics in Lindbladian SYK: a Krylov complexity perspective ⋮ The infinite Lanczos method for symmetric nonlinear eigenvalue problems ⋮ Broyden's Method for Nonlinear Eigenproblems ⋮ Compact Two-Sided Krylov Methods for Nonlinear Eigenvalue Problems

Uses Software

• JDQR
• NLEVP
• JDQZ
• NLEIGS

Cites Work

• Unnamed Item
• A linear eigenvalue algorithm for the nonlinear eigenvalue problem
• A block Newton method for nonlinear eigenvalue problems
• Nonlinear Rayleigh-Ritz iterative method for solving large scale nonlinear eigenvalue problems
• An Arnoldi method for nonlinear eigenvalue problems
• Local convergence analysis of several inexact Newton-type algorithms for general nonlinear eigenvalue problems
• Backward error and condition of polynomial eigenvalue problems
• A memory-efficient model order reduction for time-delay systems
• Handbook of Linear Algebra
• Robust Successive Computation of Eigenpairs for Nonlinear Eigenvalue Problems
• Computing a Partial Schur Factorization of Nonlinear Eigenvalue Problems Using the Infinite Arnoldi Method
• NLEVP
• An Efficient Implementation of the Nonsymmetric Lanczos Algorithm
• Templates for the Solution of Algebraic Eigenvalue Problems
• Nonlinear eigenvalue problems: a challenge for modern eigenvalue methods
• A Rational Krylov Method Based on Hermite Interpolation for Nonlinear Eigenvalue Problems
• NLEIGS: A Class of Fully Rational Krylov Methods for Nonlinear Eigenvalue Problems
• Compact Rational Krylov Methods for Nonlinear Eigenvalue Problems
• The Waveguide Eigenvalue Problem and the Tensor Infinite Arnoldi Method
• An Implementation of the Look-Ahead Lanczos Algorithm for Non-Hermitian Matrices
• Stability and Stabilization of Time-Delay Systems
• Memory-efficient Arnoldi algorithms for linearizations of matrix polynomials in Chebyshev basis
• Algorithms for the Nonlinear Eigenvalue Problem
• Preconditioned eigensolvers for large-scale nonlinear Hermitian eigenproblems with variational characterizations. I. Extreme eigenvalues

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