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Generalization of Padé approximation from rational functions to arbitrary analytic functions -- Theory


Authors: Can Evren Yarman and Garret M. Flagg
Journal: Math. Comp. 84 (2015), 1835-1860
MSC (2010): Primary 30E05, 32A17, 32A26, 65D15, 41A21; Secondary 94A12, 94A11, 32A27, 33C10, 65T99
Published electronically: January 13, 2015
MathSciNet review: 3335894
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Abstract: The Padé approximation has a long and rich history of theory and application and is known to produce excellent local approximations. We present a method for extending the basic idea of Padé approximation, that of matching a prescribed number of terms in the Taylor series expansion of a given function using rational functions, to any arbitrary function holormorphic in a neighborhood of the Taylor series expansion point. We demonstrate that providing the flexibility of using other functions in a Padé-type approximation yields highly accurate approximations having additional desirable properties. Additional properties that can be preserved in our method include comparable asymptotic behavior to the function to be approximated, or the preservation of band-limitedness in the approximation.


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Additional Information

Can Evren Yarman
Affiliation: Schlumberger, 3750 Briar Park Dr., Houston, Texas 77042
Email: cyarman@slb.com

Garret M. Flagg
Affiliation: Schlumberger, 3750 Briar Park Dr., Houston, Texas 77042
Email: GFlagg@slb.com

DOI: https://doi.org/10.1090/S0025-5718-2015-02928-7
Received by editor(s): June 13, 2013
Received by editor(s) in revised form: November 18, 2013
Published electronically: January 13, 2015
Article copyright: © Copyright 2015 American Mathematical Society