JSIAM Letters
Online ISSN : 1883-0617
Print ISSN : 1883-0609
ISSN-L : 1883-0617
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Application of the Lanczos-Phillips algorithm to continued fractions and its extension with orthogonal polynomials
Kaoru SawaYoshimasa Nakamura
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2018 Volume 10 Pages 57-60

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Abstract

The Lanczos-Phillips algorithm is a method to compute the Cholesky decomposition of Hankel matrices. This algorithm can compute the Chebyshev continued fraction from a given set of moments faster than the qd algorithm. Moreover, a new algorithm to compute the Perron continued fraction is presented with the help of orthogonal polynomials. The Cholesky decomposition of Toeplitz matrices plays a key role.

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© 2018, The Japan Society for Industrial and Applied Mathematics
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