Algorithms for Simultaneous Padé Approximations

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Abstract

We describe how to solve simultaneous Padé approximations over a power series ring K[[x]] for a field K using O~(nω - 1 d) operations in K, where d is the sought precision and $n$ is the number of power series to approximate. We develop two algorithms using different approaches. Both algorithms return a reduced sub-bases that generates the complete set of solutions to the input approximations problem that satisfy the given degree constraints. Our results are made possible by recent breakthroughs in fast computations of minimal approximant bases and Hermite Padé approximations.
Original languageEnglish
Title of host publicationProceedings of the 41st International Symposium on Symbolic and Algebraic Computation (ISSAC '16)
PublisherAssociation for Computing Machinery
Publication date2016
Pages405-412
ISBN (Print)978-1-4503-4380-0
Publication statusPublished - 2016
Event41st International Symposium on Symbolic and Algebraic Computation (ISSAC '16) - Waterloo, Ontario, Canada
Duration: 19 Jul 201622 Jul 2016
Conference number: 41
http://www.issac-symposium.org/2016/

Conference

Conference41st International Symposium on Symbolic and Algebraic Computation (ISSAC '16)
Number41
CountryCanada
CityWaterloo, Ontario
Period19/07/201622/07/2016
Internet address

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