The nonlinear eigenvalue problem
| Autor: | Stefan Güttel, Françoise Tisseur |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Numerical Analysis
Computer science General Mathematics Numerical analysis Scalar (mathematics) MathematicsofComputing_NUMERICALANALYSIS Mathematical properties 010103 numerical & computational mathematics Solver 01 natural sciences Methods of contour integration 010101 applied mathematics Algebra Nonlinear system 0101 mathematics Divide-and-conquer eigenvalue algorithm Eigenvalues and eigenvectors |
| Zdroj: | Guettel, S & Tisseur, F 2017, ' The nonlinear eigenvalue problem ', Acta Numerica, vol. 26 . https://doi.org/10.1017/S0962492917000034 |
| Popis: | Nonlinear eigenvalue problems arise in a variety of science and engineering applications, and in the past ten years there have been numerous breakthroughsin the development of numerical methods. This article surveys nonlineareigenvalue problems associated with matrix-valued functions which dependnonlinearly on a single scalar parameter, with a particular emphasis on theirmathematical properties and available numerical solution techniques. Solversbased on Newton's method, contour integration and sampling via rationalinterpolation are reviewed. Problems of selecting the appropriate parametersfor each of the solver classes are discussed and illustrated with numericalexamples. This survey also contains numerous MATLAB code snippets thatcan be used for interactive exploration of the discussed methods. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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