A rational Lanczos algorithm for model reduction

Gallivan, K.;Grimme, E;Van Dooren, Paul
(1996) Numerical Algorithms — Vol. 12, n° 1-2, p. 33-63 (1996)

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Authors
  • Gallivan, K.
    Author
  • Grimme, E
    Author
  • Van Dooren, PaulUCLouvain
    Author
Abstract
This paper presents a model reduction method for large-scale linear systems that is based on a Lanczos-type approach. A variant of the nonsymmetric Lanczos method, rational Lanczos, is shown to yield a rational interpolant (multi-point Padi approximant) for the large-scale system. An exact expression for the error in the interpolant is derived. Examples are utilized to demonstrate that the rational Lanczos method provides opportunities for significant improvements in the rate of convergence over single-point Lanczos approaches.
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Gallivan, K., Grimme, E., & Van Dooren, P. (1996). A rational Lanczos algorithm for model reduction. Numerical Algorithms, 12(1-2), 33-63. https://doi.org/10.1007/BF02141740 (Original work published 1996)