The nonlinear eigenvalue problem *

  title={The nonlinear eigenvalue problem *},
  author={Stefan G{\"u}ttel and Françoise Tisseur},
  journal={Acta Numerica},
  pages={1 - 94}
Nonlinear eigenvalue problems arise in a variety of science and engineering applications, and in the past ten years there have been numerous breakthroughs in the development of numerical methods. This article surveys nonlinear eigenvalue problems associated with matrix-valued functions which depend nonlinearly on a single scalar parameter, with a particular emphasis on their mathematical properties and available numerical solution techniques. Solvers based on Newton’s method, contour… 
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A block Newton method for nonlinear eigenvalue problems
  • D. Kressner
  • Mathematics, Computer Science
    Numerische Mathematik
  • 2009
The purpose of this work is to show that the concept of invariant pairs offers a way of representing eigenvalues and eigenvectors that is insensitive to this phenomenon, and to demonstrate the use of this concept in the development of numerical methods, a novel block Newton method is developed.
Nonlinear Eigenvalue Problems: Newton-type Methods and Nonlinear Rayleigh Functionals
Nonlinear eigenvalue problems arise in many fields of natural and engineering sciences. Theoretical and practical results are scattered in the literature and in most cases they have been developed
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Preconditioned iterative methods for a class of nonlinear eigenvalue problems
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Solving Rational Eigenvalue Problems via Linearization
It is shown that solving a class of rational eigen value problems is just as convenient and efficient as solving linear eigenvalue problems.
Solving large‐scale nonlinear eigenvalue problems by rational interpolation and resolvent sampling based Rayleigh–Ritz method
Summary Numerical solution of nonlinear eigenvalue problems (NEPs) is frequently encountered in computational science and engineering. The applicability of most existing methods is limited by the