Corpus ID: 8575527

Non-Linear Least-Squares Optimization of Rational Filters for the Solution of Interior Eigenvalue Problems

@article{Winkelmann2017NonLinearLO,
  title={Non-Linear Least-Squares Optimization of Rational Filters for the Solution of Interior Eigenvalue Problems},
  author={Jan Winkelmann and E. Napoli},
  journal={ArXiv},
  year={2017},
  volume={abs/1704.03255}
}
  • Jan Winkelmann, E. Napoli
  • Published 2017
  • Computer Science, Mathematics
  • ArXiv
  • Rational filter functions improve convergence of contour-based eigensolvers, a popular algorithm family for the solution of the interior eigenvalue problem. We present an optimization method of these rational filters in the Least-Squares sense. Our filters out-perform existing filters on a large and representative problem set, which we show on the example of FEAST. We provide a framework for (non-convex) weighted Least-Squares optimization of rational filter functions. To this end we discuss… CONTINUE READING
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    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 32 REFERENCES
    Computing Partial Spectra with Least-Squares Rational Filters
    21
    An integral method for solving nonlinear eigenvalue problems
    60
    Designing rational filter functions for solving eigenvalue problems by contour integration
    • M. Barel
    • Computer Science, Mathematics
    • 2015
    25
    Rational Krylov approximation of matrix functions: Numerical methods and optimal pole selection
    112
    Parallelization of the Rational Arnoldi Algorithm
    9
    Rational Krylov sequence methods for eigenvalue computation
    303
    Computing Eigenvalues of Real Symmetric Matrices with Rational Filters in Real Arithmetic
    35
    FEAST As A Subspace Iteration Eigensolver Accelerated By Approximate Spectral Projection
    90