The nonlinear eigenvalue problem
From MaRDI portal
Publication:4594241
DOI10.1017/S0962492917000034zbMath1377.65061OpenAlexW2598027716MaRDI QIDQ4594241
Stefan Güttel, Françoise Tisseur
Publication date: 17 November 2017
Published in: Acta Numerica (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1017/s0962492917000034
Research exposition (monographs, survey articles) pertaining to numerical analysis (65-02) Numerical interpolation (65D05) Numerical solution of nonlinear eigenvalue and eigenvector problems (65H17)
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Uses Software
Cites Work
- Approximation in eigenvalue problems for holomorphic fredholm operator functions I
- Approximation in eigenvalue problems for holomorphic fredholm operator functions Ii (Convergence Rate)
- Jentzsch-Szegö Type Theorems for the Zeros of Best Approximants
- Nonequivalence transformation of?-matrix eigenproblems and model embedding approach to model tuning
- A Jacobi–Davidson Iteration Method for Linear Eigenvalue Problems
- A Rational Krylov Method Based on Hermite Interpolation for Nonlinear Eigenvalue Problems
- Coupled Finite And Boundary Element Methods for Fluid-Solid Interaction 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
- Generalized Rational Krylov Decompositions with an Application to Rational Approximation
- The Waveguide Eigenvalue Problem and the Tensor Infinite Arnoldi Method
- A Nonlinear QR Algorithm for Banded Nonlinear Eigenvalue Problems
- Solving large‐scale nonlinear eigenvalue problems by rational interpolation and resolvent sampling based Rayleigh–Ritz method
- The Perron–Frobenius Theorem and the Ranking of Football Teams
- Stability and Stabilization of Time-Delay Systems
- Matrix Polynomials
- Scientific Computing - An Introduction using Maple and MATLAB
- Stability and Robust Stability of Linear Time-Invariant Delay Differential-Algebraic Equations
- Localization Theorems for Nonlinear Eigenvalue Problems
- Vector Spaces of Linearizations for Matrix Polynomials
- Structured Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations
- Symmetric Linearizations for Matrix Polynomials
- Functions of Matrices
- Algorithm 832
- Several properties of invariant pairs of nonlinear algebraic eigenvalue problems
- Memory-efficient Arnoldi algorithms for linearizations of matrix polynomials in Chebyshev basis
- A Numerical Method for Locating the Zeros of an Analytic Function
- ZOLOTAREV PROBLEMS CONNECTED WITH RATIONAL FUNCTIONS
- On an Approach to the Solution of the Generalized Latent Value Problem for $\lambda $-Matrices
- Algorithms for the Nonlinear Eigenvalue Problem
- Preconditioned eigensolvers for large-scale nonlinear Hermitian eigenproblems with variational characterizations. I. Extreme eigenvalues
- Nichtlineare Behandlung von Eigenwertaufgaben
- Stability of time-delay systems
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Linearizations of matrix polynomials in Bernstein bases
- Designing rational filter functions for solving eigenvalue problems by contour integration
- An integral method for solving nonlinear eigenvalue problems
- Hermitian matrix polynomials with real eigenvalues of definite type. I: Classification
- Nonlinear Rayleigh functionals
- A linear eigenvalue algorithm for the nonlinear eigenvalue problem
- Nonlinear eigenvalue problems and contour integrals
- A framework for analyzing nonlinear eigenproblems and parametrized linear systems
- The generalized eigenvalue problem and acoustic surface wave computations
- Continuation of eigenvalues and invariant pairs for parameterized nonlinear eigenvalue problems
- Chebyshev interpolation for nonlinear eigenvalue problems
- A generalized Rayleigh quotient iteration for lambda-matrices
- Detecting hyperbolic and definite matrix polynomials
- A block Newton method for nonlinear eigenvalue problems
- Pseudospectra and stability radii for analytic matrix functions with application to time-delay systems
- Trimmed linearizations for structured matrix polynomials
- Nonlinear Rayleigh-Ritz iterative method for solving large scale nonlinear eigenvalue problems
- An SVD-approach to Jacobi-Davidson solution of nonlinear Helmholtz eigenvalue problems
- Solving nonlinear eigenvalue problems by algorithmic differentiation
- Analytic matrix functions with prescribed local data
- The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices
- A projection method for generalized eigenvalue problems using numerical integration.
- More on pseudospectra for polynomial eigenvalue problems and applications in control theory
- An Arnoldi method for nonlinear eigenvalue problems
- Photonic band structure calculations using nonlinear eigenvalue techniques
- Two-sided and alternating Jacobi-Davidson
- On the numerical solution of nonlinear eigenvalue problems
- Solution of large eigenvalue problems in electronic structure calculations
- Jacobi-Davidson type methods for generalized eigenproblems and polynomial eigenproblems
- Local convergence analysis of several inexact Newton-type algorithms for general nonlinear eigenvalue problems
- On locating clusters of zeros of analytic functions
- ZEAL: A mathematical software package for computing zeros of analytic functions
- Backward error and condition of polynomial eigenvalue problems
- Convergence of rational interpolants
- On the local theory of regular analytic matrix functions
- Preconditioned iterative methods for a class of nonlinear eigenvalue problems
- A spatially adaptive iterative method for a class of nonlinear operator eigenproblems
- Local convergence of Newton-like methods for degenerate eigenvalues of nonlinear eigenproblems. I. Classical algorithms
- Solving acoustic nonlinear eigenvalue problems with a contour integral method
- The solution of characteristic value-vector problems by Newton's method
- Variationsprinzipien bei nichtlinearen Eigenwertaufgaben
- Mehrparametrige und nichtlineare Eigenwertaufgaben
- On interpolation by rational functions
- A minimax theory for overdamped systems
- Structured Pseudospectra for Polynomial Eigenvalue Problems, with Applications
- The Quadratic Eigenvalue Problem
- A Krylov--Schur Algorithm for Large Eigenproblems
- Stability Analysis of the Two-level Orthogonal Arnoldi Procedure
- A Newton-Type Method with Nonequivalence Deflation for Nonlinear Eigenvalue Problems Arising in Photonic Crystal Modeling
- Linearizations for Rational Matrix Functions and Rosenbrock System Polynomials
- Parallel Krylov Solvers for the Polynomial Eigenvalue Problem in SLEPc
- Fiedler-comrade and Fiedler--Chebyshev pencils
- A numerical method for nonlinear eigenvalue problems using contour integrals
- Rational Krylov approximation of matrix functions: Numerical methods and optimal pole selection
- Robust Successive Computation of Eigenpairs for Nonlinear Eigenvalue Problems
- Boundary element approximation for Maxwell's eigenvalue problem
- Computing a Partial Schur Factorization of Nonlinear Eigenvalue Problems Using the Infinite Arnoldi Method
- The Infinite Arnoldi Method and an Application to Time-Delay Systems with Distributed Delays
- Numerical Algorithms Based on Analytic Function Values at Roots of Unity
- The Exponentially Convergent Trapezoidal Rule
- Polynomial Eigenvalue Problems: Theory, Computation, and Structure
- A Padé approximate linearization algorithm for solving the quadratic eigenvalue problem with low-rank damping
- A rank-exploiting infinite Arnoldi algorithm for nonlinear eigenvalue problems
- Parallel iterative refinement in polynomial eigenvalue problems
- MATLAB Guide, Third Edition
- Numerical Methods for Large Eigenvalue Problems
- Solving Rational Eigenvalue Problems via Linearization
- A minmax principle for nonlinear eigenproblems depending continuously on the eigenparameter
- A projection method for nonlinear eigenvalue problems using contour integrals
- Derivatives of Eigenvalues and Eigenvectors of Matrix Functions
- An Iterative Method for Computing the Pseudospectral Abscissa for a Class of Nonlinear Eigenvalue Problems
- NLEVP
- SLEPc
- Evaluating Derivatives
- Continuation of Invariant Subspaces for Parameterized Quadratic Eigenvalue Problems
- Linearization of matrix polynomials expressed in polynomial bases
- Computing $A^\alpha, \log(A)$, and Related Matrix Functions by Contour Integrals
- A method for eigenvalues of sparse λ-matrices
- Matrix Analysis
- Residual Inverse Iteration for the Nonlinear Eigenvalue Problem
- GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
- Inverse Iteration, Ill-Conditioned Equations and Newton’s Method
- A minimax principle for nonlinear eigenvalue problems with applications to nonoverdamped systems
- Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
- Local and Global Equivalence of Meromorphic Operator Functions Part II
- Using Generalized Cayley Transformations within an Inexact Rational Krylov Sequence Method
- Computing an Eigenvector with Inverse Iteration
- QMRPACK
- ARPACK Users' Guide
- Rational Krylov: A Practical Algorithm for Large Sparse Nonsymmetric Matrix Pencils
- Templates for the Solution of Algebraic Eigenvalue Problems
- Nonlinear eigenvalue problems: a challenge for modern eigenvalue methods