ACM Transactions on Mathematical Software (TOMS), ISSN 0098-3500, 02/2013, Volume 39, Issue 2, pp. 1 - 28

We present a collection of 52 nonlinear eigenvalue problems in the form of a MATLAB toolbox. The collection contains problems from models of real-life...

rational eigenvalue problem | hyperbolic | Test problem | Octave | Hermitian | MATLAB | benchmark | odd | palindromic | symmetric | nonlinear eigenvalue problem | even | proportionally-damped | gyroscopic | polynomial eigenvalue problem | quadratic eigenvalue problem | overdamped | elliptic | Rational eigenvalue problem | Nonlinear eigenvalue problem | Odd | Gyroscopic | Overdamped | Palindromic | Hyperbolic | Proportionally-damped | Benchmark | Quadratic eigenvalue problem | Elliptic | Even | Symmetric | Polynomial eigenvalue problem | MATHEMATICS, APPLIED | APPROXIMATION | STABILITY | SENSITIVITY | EQUATIONS | MATRIX POLYNOMIALS | REPRODUCIBLE RESEARCH | PERTURBATION | COMPUTER SCIENCE, SOFTWARE ENGINEERING | Algorithms | SYSTEMS | PSEUDOSPECTRA | Performance | EIGENPROBLEMS | Eigenvalues | Nonlinear theories | Research | Classification

rational eigenvalue problem | hyperbolic | Test problem | Octave | Hermitian | MATLAB | benchmark | odd | palindromic | symmetric | nonlinear eigenvalue problem | even | proportionally-damped | gyroscopic | polynomial eigenvalue problem | quadratic eigenvalue problem | overdamped | elliptic | Rational eigenvalue problem | Nonlinear eigenvalue problem | Odd | Gyroscopic | Overdamped | Palindromic | Hyperbolic | Proportionally-damped | Benchmark | Quadratic eigenvalue problem | Elliptic | Even | Symmetric | Polynomial eigenvalue problem | MATHEMATICS, APPLIED | APPROXIMATION | STABILITY | SENSITIVITY | EQUATIONS | MATRIX POLYNOMIALS | REPRODUCIBLE RESEARCH | PERTURBATION | COMPUTER SCIENCE, SOFTWARE ENGINEERING | Algorithms | SYSTEMS | PSEUDOSPECTRA | Performance | EIGENPROBLEMS | Eigenvalues | Nonlinear theories | Research | Classification

Journal Article

Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 10/2016, Volume 310, pp. 33 - 57

A new algorithm, denoted by RSRR, is presented for solving large-scale nonlinear eigenvalue problems (NEPs) with a focus on improving the robustness and...

Finite element method | Rayleigh–Ritz procedure | Nonlinear eigenvalue problems | Boundary element method | BURTON-MILLER FORMULATION | INTEGRAL METHOD | LINEARIZATIONS | BOUNDARY-ELEMENT METHOD | Rayleigh-Ritz procedure | INTERPOLATION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | FINITE | ENGINEERING, MULTIDISCIPLINARY | PROJECTION METHOD | SYSTEMS | RATIONAL KRYLOV METHODS | VISCOELASTIC STRUCTURES | Methods | Algorithms | Mathematics - Numerical Analysis

Finite element method | Rayleigh–Ritz procedure | Nonlinear eigenvalue problems | Boundary element method | BURTON-MILLER FORMULATION | INTEGRAL METHOD | LINEARIZATIONS | BOUNDARY-ELEMENT METHOD | Rayleigh-Ritz procedure | INTERPOLATION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | FINITE | ENGINEERING, MULTIDISCIPLINARY | PROJECTION METHOD | SYSTEMS | RATIONAL KRYLOV METHODS | VISCOELASTIC STRUCTURES | Methods | Algorithms | Mathematics - Numerical Analysis

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 2014, Volume 47, Issue 23, pp. 235204 - 15

This paper presents an asymptotic study of the differential equation y' (x) = cos[pi xy(x)] subject to the initial condition y(0) = a. While this differential...

semiclassical | separatrix | WKB, asymptotic | asymptotic | eigenvalue | WKB | PARTIAL SUMS | PHYSICS, MULTIDISCIPLINARY | POWER SERIES | PHYSICS, MATHEMATICAL | Asymptotic properties | Mathematical analysis | Differential equations | Eigenvalues | Nonlinearity | Constants | Mathematical models | Schroedinger equation

semiclassical | separatrix | WKB, asymptotic | asymptotic | eigenvalue | WKB | PARTIAL SUMS | PHYSICS, MULTIDISCIPLINARY | POWER SERIES | PHYSICS, MATHEMATICAL | Asymptotic properties | Mathematical analysis | Differential equations | Eigenvalues | Nonlinearity | Constants | Mathematical models | Schroedinger equation

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 05/2012, Volume 436, Issue 10, pp. 3839 - 3863

We propose a numerical method for computing all eigenvalues (and the corresponding eigenvectors) of a nonlinear holomorphic eigenvalue problem that lie within...

Contour integrals | Nonlinear eigenvalue problems | Numerical methods | MATHEMATICS | MATHEMATICS, APPLIED | MATRIX FUNCTIONS | PROJECTION METHOD | ARNOLDI METHOD

Contour integrals | Nonlinear eigenvalue problems | Numerical methods | MATHEMATICS | MATHEMATICS, APPLIED | MATRIX FUNCTIONS | PROJECTION METHOD | ARNOLDI METHOD

Journal Article

Mechanical Systems and Signal Processing, ISSN 0888-3270, 08/2019, Volume 129, pp. 629 - 644

•Local damage identification using non-negative least squares is investigated.•Unique non-negative and sparse solutions to ill-posed linearized inverse...

Non-negative constraint | Damage identification | Sparsity | Ill-posed inverse | Constrained nonlinear least squares | Finite element model updating | MODAL PARAMETERS | III-posed inverse | STRUCTURAL DAMAGE | REGULARIZATION | ENGINEERING, MECHANICAL | Computer simulation | Performance assessment | Truncation errors | Noise measurement | Optimization | Finite element method | Damage detection | Eigenvalues | Stiffness | Ill-posed problems (mathematics) | Model updating | Eigen values | Linearization

Non-negative constraint | Damage identification | Sparsity | Ill-posed inverse | Constrained nonlinear least squares | Finite element model updating | MODAL PARAMETERS | III-posed inverse | STRUCTURAL DAMAGE | REGULARIZATION | ENGINEERING, MECHANICAL | Computer simulation | Performance assessment | Truncation errors | Noise measurement | Optimization | Finite element method | Damage detection | Eigenvalues | Stiffness | Ill-posed problems (mathematics) | Model updating | Eigen values | Linearization

Journal Article

International Journal for Numerical Methods in Engineering, ISSN 0029-5981, 05/2017, Volume 110, Issue 8, pp. 776 - 800

Summary Numerical solution of nonlinear eigenvalue problems (NEPs) is frequently encountered in computational science and engineering. The applicability of...

boundary element methods | eigenvalue problems | Rayleigh–Ritz procedure | finite element methods | nonlinear solvers | Rayleigh-Ritz procedure | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | KRYLOV METHODS | ROOTS | Rayleigh-Ritz method | Interpolation | Robustness (mathematics) | Mathematical analysis | Eigenvalues | Nonlinearity | Mathematical models | Sampling

boundary element methods | eigenvalue problems | Rayleigh–Ritz procedure | finite element methods | nonlinear solvers | Rayleigh-Ritz procedure | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | KRYLOV METHODS | ROOTS | Rayleigh-Ritz method | Interpolation | Robustness (mathematics) | Mathematical analysis | Eigenvalues | Nonlinearity | Mathematical models | Sampling

Journal Article

Communications on Pure and Applied Analysis, ISSN 1534-0392, 05/2019, Volume 18, Issue 3, pp. 1403 - 1431

We consider perturbations of nonlinear eigenvalue problems driven by a nonhomogeneous differential operator plus an indefinite potential. We consider both...

Nonhomogeneous differential operator | Nonlinear maximum principle | Superlinear perturbation | Sublinear | Minimal positive solution | Comparison principle | Nonlinear regularity | minimal positive solution | P-LAPLACIAN-TYPE | EXISTENCE | MATHEMATICS | nonlinear maximum principle | MATHEMATICS, APPLIED | sublinear and superlinear perturbation | MULTIPLICITY | nonlinear regularity | comparison principle | Mathematics - Analysis of PDEs

Nonhomogeneous differential operator | Nonlinear maximum principle | Superlinear perturbation | Sublinear | Minimal positive solution | Comparison principle | Nonlinear regularity | minimal positive solution | P-LAPLACIAN-TYPE | EXISTENCE | MATHEMATICS | nonlinear maximum principle | MATHEMATICS, APPLIED | sublinear and superlinear perturbation | MULTIPLICITY | nonlinear regularity | comparison principle | Mathematics - Analysis of PDEs

Journal Article

Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, 07/2015, Volume 25, Issue 8, pp. 1421 - 1445

The aim of this paper is to develop a virtual element method for the two-dimensional Steklov eigenvalue problem. We propose a discretization by means of the...

error estimates | Steklov eigenvalue problem | Virtual element method | CONTAINERS | RESONANT FREQUENCIES | MATHEMATICS, APPLIED | APPROXIMATION | FLUID | REGULARITY | FORMULATION | BAFFLE

error estimates | Steklov eigenvalue problem | Virtual element method | CONTAINERS | RESONANT FREQUENCIES | MATHEMATICS, APPLIED | APPROXIMATION | FLUID | REGULARITY | FORMULATION | BAFFLE

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 01/2016, Volume 292, pp. 526 - 540

In this paper Beyn’s algorithm for solving nonlinear eigenvalue problems is given a new interpretation and a variant is designed in which the required...

Contour integrals | Canonical polyadic decomposition | Filter function | Keldysh’ theorem | Beyn’s algorithm | Nonlinear eigenvalue problems | Keldysh'theorem | Beyn's algorithm | MULTILINEAR-ALGEBRA | MATHEMATICS, APPLIED | NUMERICAL-METHOD | Keldysh' theorem | PROJECTION | EIGENSOLVER | FEAST | ANALYTIC-FUNCTION | Algorithms | Tensors | Shape | Integrals | Mathematical analysis | Eigenvalues | Nonlinearity | Mathematical models

Contour integrals | Canonical polyadic decomposition | Filter function | Keldysh’ theorem | Beyn’s algorithm | Nonlinear eigenvalue problems | Keldysh'theorem | Beyn's algorithm | MULTILINEAR-ALGEBRA | MATHEMATICS, APPLIED | NUMERICAL-METHOD | Keldysh' theorem | PROJECTION | EIGENSOLVER | FEAST | ANALYTIC-FUNCTION | Algorithms | Tensors | Shape | Integrals | Mathematical analysis | Eigenvalues | Nonlinearity | Mathematical models

Journal Article

ELECTRONIC JOURNAL OF LINEAR ALGEBRA, ISSN 1537-9582, 05/2019, Volume 35, pp. 187 - 203

This work deals with the eigenvalue analysis of a rational matrix-valued function subject to complementarity constraints induced by a polyhedral cone K. The...

MATHEMATICS | Rational matrix-valued function | Polyhedral cone | Facial reduction technique | Complementarity problem | LINEARIZATIONS | Linearization method | Nonlinear eigenvalue problem

MATHEMATICS | Rational matrix-valued function | Polyhedral cone | Facial reduction technique | Complementarity problem | LINEARIZATIONS | Linearization method | Nonlinear eigenvalue problem

Journal Article

Rivista di Matematica della Universita di Parma, ISSN 0035-6298, 2014, Volume 5, Issue 2, pp. 373 - 386

Journal Article

SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, 2017, Volume 38, Issue 2, pp. 599 - 620

We contribute to the perturbation theory of nonlinear eigenvalue problems in three ways. First, we extend the formula for the sensitivity of a simple...

Asymptotic distribution of eigenvalues and eigenfunctions | Perturbations of nonlinear operators | Nonlinear eigenvalue problems | Matrix and operator equations | Systems of functional equations and inequalities | nonlinear eigenvalue problems | matrix and operator equations | ANALYTIC MATRIX FUNCTIONS | MATHEMATICS, APPLIED | systems of functional equations and inequalities | asymptotic distribution of eigenvalues and eigenfunctions | STABILITY | PERTURBATION | EQUATIONS | perturbations of nonlinear operators | SYSTEMS | ROOTS

Asymptotic distribution of eigenvalues and eigenfunctions | Perturbations of nonlinear operators | Nonlinear eigenvalue problems | Matrix and operator equations | Systems of functional equations and inequalities | nonlinear eigenvalue problems | matrix and operator equations | ANALYTIC MATRIX FUNCTIONS | MATHEMATICS, APPLIED | systems of functional equations and inequalities | asymptotic distribution of eigenvalues and eigenfunctions | STABILITY | PERTURBATION | EQUATIONS | perturbations of nonlinear operators | SYSTEMS | ROOTS

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 01/2020, Volume 190, p. 111607

We consider a nonlinear eigenvalue problem for some elliptic equations governed by general operators including the p-Laplacian. The natural framework in which...

Harnack inequality | Nonlinear eigenvalue problems | Orlicz–Sobolev spaces | MATHEMATICS | MATHEMATICS, APPLIED | Orlicz-Sobolev spaces | 1ST EIGENVALUE | DIFFERENTIAL-OPERATORS | Eigenvalues | Maximum principle | Elliptic functions | Mathematical analysis | Sobolev space | Eigen values

Harnack inequality | Nonlinear eigenvalue problems | Orlicz–Sobolev spaces | MATHEMATICS | MATHEMATICS, APPLIED | Orlicz-Sobolev spaces | 1ST EIGENVALUE | DIFFERENTIAL-OPERATORS | Eigenvalues | Maximum principle | Elliptic functions | Mathematical analysis | Sobolev space | Eigen values

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 10/2019, Volume 578, pp. 272 - 296

Sylvester's law of inertia states that the number of positive, negative and zero eigenvalues of Hermitian matrices is preserved under congruence...

Generalized indefinite eigenvalue problem | Number of eigenvalues in an interval | Sylvester's law of inertia | Congruence transformation | Nonlinear eigenvalue problems | MATHEMATICS, APPLIED | CANONICAL-FORMS | DECOMPOSITION | LINEARIZATIONS | EQUIVALENCE | VECTOR-SPACES | MATHEMATICS | MATRIX POLYNOMIALS | Mathematical analysis | Legislation | Eigenvalues | Inertia | Transformations | Matrix methods | Eigen values

Generalized indefinite eigenvalue problem | Number of eigenvalues in an interval | Sylvester's law of inertia | Congruence transformation | Nonlinear eigenvalue problems | MATHEMATICS, APPLIED | CANONICAL-FORMS | DECOMPOSITION | LINEARIZATIONS | EQUIVALENCE | VECTOR-SPACES | MATHEMATICS | MATRIX POLYNOMIALS | Mathematical analysis | Legislation | Eigenvalues | Inertia | Transformations | Matrix methods | Eigen values

Journal Article

SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, 2014, Volume 35, Issue 3, pp. 819 - 834

This work considers eigenvalue problems that are nonlinear in the eigenvalue parameter. Given such a nonlinear eigenvalue problem T, we are concerned with...

Backward error | Analytic matrix-valued function | Sylvester-like operator | Nonlinear eigenvalue problem | MATRIX | MATHEMATICS, APPLIED | MULTIPLE-EIGENVALUES | backward error | OPTIMIZATION | analytic matrix-valued function | STRUCTURED PSEUDOSPECTRA | CRITICAL-POINTS | nonlinear eigenvalue problem | Permissible error | Algebra | Perturbation methods | Norms | Eigenvalues | Nonlinearity | Constants | Optimization

Backward error | Analytic matrix-valued function | Sylvester-like operator | Nonlinear eigenvalue problem | MATRIX | MATHEMATICS, APPLIED | MULTIPLE-EIGENVALUES | backward error | OPTIMIZATION | analytic matrix-valued function | STRUCTURED PSEUDOSPECTRA | CRITICAL-POINTS | nonlinear eigenvalue problem | Permissible error | Algebra | Perturbation methods | Norms | Eigenvalues | Nonlinearity | Constants | Optimization

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 10/2014, Volume 274, pp. 681 - 694

Over the past several years a number of papers have been written describing modern techniques for numerically computing the dominant eigenvalue of the neutron...

Anderson acceleration | Nonlinear Krylov acceleration | Moment-based acceleration | k-eigenvalue problem | Jacobian-free Newton–Krylov | Neutron transport | Jacobian-free Newton-Krylov | K-eigenvalue problem | NEWTONS METHOD | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NONLINEAR ACCELERATION | PHYSICS, MATHEMATICAL | Comparative analysis | Methods | Algorithms | Computation | Categories | Mathematical analysis | Eigenvalues | Mathematical models | Transport | Diffusion | Acceleration | ACCELERATION | NEUTRON TRANSPORT | EIGENVALUES | MATHEMATICAL SOLUTIONS | DIFFUSION EQUATIONS | NONLINEAR PROBLEMS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | IMPLEMENTATION | DIFFUSION | ALGORITHMS | COMPARATIVE EVALUATIONS

Anderson acceleration | Nonlinear Krylov acceleration | Moment-based acceleration | k-eigenvalue problem | Jacobian-free Newton–Krylov | Neutron transport | Jacobian-free Newton-Krylov | K-eigenvalue problem | NEWTONS METHOD | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NONLINEAR ACCELERATION | PHYSICS, MATHEMATICAL | Comparative analysis | Methods | Algorithms | Computation | Categories | Mathematical analysis | Eigenvalues | Mathematical models | Transport | Diffusion | Acceleration | ACCELERATION | NEUTRON TRANSPORT | EIGENVALUES | MATHEMATICAL SOLUTIONS | DIFFUSION EQUATIONS | NONLINEAR PROBLEMS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | IMPLEMENTATION | DIFFUSION | ALGORITHMS | COMPARATIVE EVALUATIONS

Journal Article

International Journal of Bifurcation and Chaos, ISSN 0218-1274, 06/2019, Volume 29, Issue 6, p. 1950084

We focus on the structure of the solution set for the nonlinear equation u = L ( λ ) u + H ( λ , u ) , where L ( ⋅ ) and H ( λ , u ) are continuous operators....

homogeneous operator | P-LAPLACIAN | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Monge-Ampere equation | REGULARITY | MULTIDISCIPLINARY SCIENCES | 1ST EIGENVALUE | DIRICHLET PROBLEM | REAL | ELLIPTIC-EQUATIONS | one-sign solution | Global bifurcation

homogeneous operator | P-LAPLACIAN | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Monge-Ampere equation | REGULARITY | MULTIDISCIPLINARY SCIENCES | 1ST EIGENVALUE | DIRICHLET PROBLEM | REAL | ELLIPTIC-EQUATIONS | one-sign solution | Global bifurcation

Journal Article

BIT Numerical Mathematics, ISSN 0006-3835, 12/2012, Volume 52, Issue 4, pp. 933 - 951

This work is concerned with numerical methods for matrix eigenvalue problems that are nonlinear in the eigenvalue parameter. In particular, we focus on...

Boundary element formulation | 47J10 | Computational Mathematics and Numerical Analysis | Numeric Computing | 41A10 | Krylov subspace method | Mathematics, general | Mathematics | 35P30 | Nonlinear eigenvalue problem | Chebyshev interpolation | Linearization | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED

Boundary element formulation | 47J10 | Computational Mathematics and Numerical Analysis | Numeric Computing | 41A10 | Krylov subspace method | Mathematics, general | Mathematics | 35P30 | Nonlinear eigenvalue problem | Chebyshev interpolation | Linearization | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED

Journal Article

SIAM Review, ISSN 0036-1445, 2015, Volume 57, Issue 4, pp. 585 - 607

Let T : Omega -> C-nXn be a matrix-valued function that is analytic on some simply connected domain Omega subset of C. A point lambda is an element of Omega is...

Perturbation theory | Pseudospectra | Nonlinear eigenvalue problems | Gershgorin's theorem | nonlinear eigenvalue problems | MATHEMATICS, APPLIED | MATRIX FUNCTIONS | perturbation theory | BACKWARD ERROR | ALGEBRAIC-CURVES | PERTURBATION | pseudospectra | ALGORITHMS | Eigenvalues | Usage | Perturbation (Mathematics) | Differential equations

Perturbation theory | Pseudospectra | Nonlinear eigenvalue problems | Gershgorin's theorem | nonlinear eigenvalue problems | MATHEMATICS, APPLIED | MATRIX FUNCTIONS | perturbation theory | BACKWARD ERROR | ALGEBRAIC-CURVES | PERTURBATION | pseudospectra | ALGORITHMS | Eigenvalues | Usage | Perturbation (Mathematics) | Differential equations

Journal Article

Journal of Computational Science, ISSN 1877-7503, 07/2018, Volume 27, pp. 107 - 117

•The Cauchy integral from the FEAST algorithm can be modified to solve nonlinear eigenvalue problems.•FEAST for nonlinear eigenvalue problems iteratively...

Quadratic eigenvalue problem | FEAST | Residual inverse iteration | Polynomial eigenvalue problem | Contour integration | Nonlinear eigenvalue problem | ITERATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | COMPUTER SCIENCE, THEORY & METHODS | ARNOLDI METHOD | Eigenvalues | Algorithms | Research

Quadratic eigenvalue problem | FEAST | Residual inverse iteration | Polynomial eigenvalue problem | Contour integration | Nonlinear eigenvalue problem | ITERATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | COMPUTER SCIENCE, THEORY & METHODS | ARNOLDI METHOD | Eigenvalues | Algorithms | Research

Journal Article

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