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A RATIONAL KRYLOV METHOD BASED ON HERMITE INTERPOLATION FOR NONLINEAR EIGENVALUE PROBLEMS
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DOI：10.1137/120877556.png)
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Abstract
En 中文
This paper proposes a new rational Krylov method for solving the nonlinear eigenvalue problem: A(lambda) x = 0. The method approximates A(lambda) by Hermite interpolation where the degree of the interpolating polynomial and the interpolation points are not fixed in advance. It uses a companion-type reformulation to obtain a linear generalized eigenvalue problem (GEP). To this GEP we apply a rational Krylov method that preserves the structure. The companion form grows in each iteration and the interpolation points are dynamically chosen. Each iteration requires a linear system solve with A(sigma), where sigma is the last interpolation point. The method is illustrated by small-and large-scale numerical examples. In particular, we illustrate that the method is fully dynamic and can be used as a global search method as well as a local refinement method. In the last case, we compare the method to Newton's method and illustrate that we can achieve an even faster convergence rate.
Keywords:
rational Krylov
Newton polynomials
Hermite interpolation
nonlinear eigenvalue problem
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