research-article

NLEVP: A Collection of Nonlinear Eigenvalue Problems

Authors:

Nicholas J. Higham,

Volker Mehrmann,

Christian Schröder,

Françoise TisseurAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 39, Issue 2

Article No.: 7, Pages 1 - 28

https://doi.org/10.1145/2427023.2427024

Published: 01 February 2013 Publication History

Abstract

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 applications as well as ones constructed specifically to have particular properties. A classification is given of polynomial eigenvalue problems according to their structural properties. Identifiers based on these and other properties can be used to extract particular types of problems from the collection. A brief description of each problem is given. NLEVP serves both to illustrate the tremendous variety of applications of nonlinear eigenvalue problems and to provide representative problems for testing, tuning, and benchmarking of algorithms and codes.

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Li DPolizzi E(2025) Nonlinear eigenvalue algorithm for quasiparticle equations Physical Review B10.1103/PhysRevB.111.045137111:4Online publication date: 17-Jan-2025
https://doi.org/10.1103/PhysRevB.111.045137
Melman A(2025)Zero exclusion sectors for polynomials whose coefficients exhibit a +/-/+ sign patternProceedings of the American Mathematical Society10.1090/proc/17070153:3(1109-1120)Online publication date: 24-Jan-2025
https://doi.org/10.1090/proc/17070
Amparan ABaragaña IMarcaida SRoca A(2025)Row or column completion of polynomial matrices of given degree IILinear Algebra and its Applications10.1016/j.laa.2024.12.004708(252-279)Online publication date: Mar-2025
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Index Terms

NLEVP: A Collection of Nonlinear Eigenvalue Problems
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
      1. Linear algebra algorithms
2. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
      1. Computations on matrices
  2. Mathematical software

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cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 39, Issue 2

February 2013

151 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/2427023

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Published: 01 February 2013

Accepted: 01 March 2012

Revised: 01 December 2011

Received: 01 November 2010

Published in TOMS Volume 39, Issue 2

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