arXiv Open Access 2016

Algorithms for Simultaneous Padé Approximations

Johan S. R. Nielsen Arne Storjohann

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Abstrak

We describe how to solve simultaneous Padé approximations over a power series ring $K[[x]]$ for a field $K$ using $O~(n^{ω- 1} d)$ 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.

Topik & Kata Kunci

cs.SC

Penulis (2)

Johan S. R. Nielsen

Arne Storjohann

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APA MLA BibTeX

Nielsen, J.S.R., Storjohann, A. (2016). Algorithms for Simultaneous Padé Approximations. https://arxiv.org/abs/1602.00836

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Informasi Jurnal

Tahun Terbit: 2016
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓