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A uniform approach for Hermite Padé and simultaneous Padé approximants and their matrix-type generalizations

1992
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Numerical Algorithms
*

This includes descriptions of vector and matrix

doi:10.1007/bf02141914
fatcat:5wyrxru4dndxtmhwhtfyb47rha
*Padé**approximants*along with generalizations of*simultaneous*and*Hermite**Padé**approximants*. ... This paper introduces the notion of a power*Hermite**Padé**approximant*, a generalization of the classical scalar*Hermite**Padé**approximant*. ... example, to derive*algorithms*where both types of*approximants*are computed*simultaneously*. ...##
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Page 1563 of Mathematical Reviews Vol. , Issue 93c
[page]

1993
*
Mathematical Reviews
*

The

*algorithm*provides a method*for*obtaining ma- trix*Padé*, matrix*Hermite**Padé*and matrix*simultaneous**Padé**approximants*. ... The recurrence relation results in a fast*algorithm**for*calculating a*Padé*-*Hermite**approximant*of any given type. ...##
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Fraction-free computation of simultaneous padé approximants

2009
*
Proceedings of the 2009 international symposium on Symbolic and algebraic computation - ISSAC '09
*

How to Compute

doi:10.1145/1576702.1576708
dblp:conf/issac/BeckermannL09
fatcat:k5laijlphzgmzibdo5ak3y2ip4
*Simultaneous**Padé**Approximants*(1) linear system of equations*for*coefficients of U i (z), V (z) system has 'special' structured coefficient matrix fast*algorithms*take advantage of 'special ... ' structure (2) represent as a vector*Hermite*-*Padé*problem find order basis*for*problem fast*algorithms*order bases find all solutions of these approx problems (3) todays : solve problem via order bases ...##
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Page 5067 of Mathematical Reviews Vol. , Issue 93i
[page]

1993
*
Mathematical Reviews
*

This includes descriptions of vector and matrix

*Padé**approximants*along with generalizations of*simultaneous*and*Hermite**Padé**approximants*. ... {*For*the entire collection see MR 93g:65008.} 93i1:65026 65D15 41A21 Beckermann, Bernhard (D-HANN-AM); Labahn, George (3-WTRL-C) A uniform approach*for**Hermite**Padé*and*simultaneous**Padé**approximants*and ...##
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Page 3499 of Mathematical Reviews Vol. , Issue 93g
[page]

1993
*
Mathematical Reviews
*

rational

*Hermite*interpolation (29-44); Bernhard Beckermann and George Labahn, A uniform approach*for**Hermite**Padé*and*simultaneous**Padé**approximants*and their matrix-type generalizations (45-54); T. ... Lu- binsky, Convergence of*simultaneous**Hermite*-*Padé**approximants*to the n-tuple of g-hypergeometric series {1®1((23)); z)}"_, (185- 192); Mariano Gasca and José J. ...##
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Page 3577 of Mathematical Reviews Vol. , Issue 95f
[page]

1995
*
Mathematical Reviews
*

and

*Hermite**Padé**approximants*[Numer. ... The considerations in this paper are based on this generalized form of the classical scalar*Hermite**Padé**approximation*problem, power*Hermite**Padé**approximation*. ...##
###
Page 1662 of Mathematical Reviews Vol. , Issue 97C
[page]

1997
*
Mathematical Reviews
*

The article proposes an

*algorithm*that solves two dual vector*Padé*-*Hermite*problems at the same time, returning dual basis matrices of the respective solution spaces.” ... We also show that the classical duality between*Padé*-*Hermite*problems of type I and type II is a special case of vector*Padé*-*Hermite*duality. ...##
###
Page 4456 of Mathematical Reviews Vol. , Issue 97G
[page]

1997
*
Mathematical Reviews
*

*Simultaneous*

*Padé*(SP)

*approximation*is a dual problem. ... and

*simultaneous*

*Padé*systems. ...

##
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On the theory and computation of nonperfect padé-hermite approximants

1992
*
Journal of Computational and Applied Mathematics
*

The recurrence relation results in a fast

doi:10.1016/0377-0427(92)90206-d
fatcat:dppxuwdjvne7rbws4pivw5tara
*algorithm**for*calculating a Pad&*Hermite**approximant*of any given type. ...*For*a vector of k + 1 power series we introduce two new types of rational*approximations*, the weak Pad&*Hermite*form and the weak Pad&*Hermite*fraction. ... When k = 1, Pad&*Hermite*approxi-mants reduce to*Pade**approximants*, and the*algorithm*becomes that of [5] and the scalar*algorithm*of [16] . ...##
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A fast, reliable algorithm for calculating Pade´-Hermite forms

1989
*
Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation - ISSAC '89
*

This complexity is the same as that of other fast

doi:10.1145/74540.74553
dblp:conf/issac/CabayL89
fatcat:oi3sr3kfjza2lk2lpugv752nwu
*algorithms**for*computing Pad&*Hermite**approximants*. ... We present a new fast*algorithm**for*the calculation of a Pad&*Hermite*form*for*a vector of power series. ... A WPHFr can be interpreted as providing a a set of*simultaneous**Pade**approximants**for*the quotient power series &(z)/&(z) (cf., de Bruin[2]). ...##
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Computation of Numerical Padé–Hermite and Simultaneous Padé Systems II: A Weakly Stable Algorithm

1996
*
SIAM Journal on Matrix Analysis and Applications
*

of

doi:10.1137/s0895479894268695
fatcat:fb53lzr55rdqdedw4yl57jmoh4
*Padé*-*Hermite*and*simultaneous**Padé*systems and, thereby, also*for*the numerical inversion of striped and mosaic Sylvester matrices. ... The near inverses are expressed in terms of numerical*Padé*-*Hermite*systems and*simultaneous**Padé*systems. ...*Padé*-*Hermite*and*simultaneous**Padé**approximants*were introduced by*Hermite*in the last century and has been widely studied by several authors (*for*a bibliography, see,*for*example [1, 2, 3, 4, 15] ). ...##
###
Page 1099 of Mathematical Reviews Vol. , Issue 82c
[page]

1982
*
Mathematical Reviews
*

*algorithms*

*for*the computation of

*Padé*and c-tables in the presence of blocks, and

*algorithms*

*for*the choice of the best PA when a number of Taylor coefficients of a power series are given. ... New elements are presented, most important of which are the algebraic theory of

*Padé*

*approximation*in the presence of blocks, the analysis of the convergence of the e-

*algorithm*via

*Padé*

*approximation*, ...

##
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Computation of Numerical Padé–Hermite and Simultaneous Padé Systems I: Near Inversion of Generalized Sylvester Matrices

1996
*
SIAM Journal on Matrix Analysis and Applications
*

of

doi:10.1137/s0895479894268683
fatcat:u72p6zysibgynkwqtdxm3p2mfm
*Padé*-*Hermite*and*simultaneous**Padé*systems and, thereby, also*for*the numerical inversion of striped and mosaic Sylvester matrices. ... The near inverses are expressed in terms of numerical*Padé*-*Hermite*systems and*simultaneous**Padé*systems. ...*Padé*-*Hermite*and*simultaneous**Padé**approximants*were introduced by*Hermite*in the last century and has been widely studied by several authors (*for*a bibliography, see,*for*example [1, 2, 3, 4, 15] ). ...##
###
Algorithms for Simultaneous Padé Approximations

2016
*
Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation - ISSAC '16
*

We describe how to solve

doi:10.1145/2930889.2930933
dblp:conf/issac/RosenkildeS16
fatcat:ew5jndxpovg2hijommcgiouuau
*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 ... Our results are made possible by recent breakthroughs in fast computations of minimal*approximant*bases and*Hermite**Padé**approximations*. ... The authors would like to thank George Labahn*for*valuable discussions, and*for*making us aware of the*Hermite*-*Simultaneous**Padé*duality. ...##
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Foreword to the proceedings of the OrthoQuad 2014 conference

2015
*
Journal of Computational and Applied Mathematics
*

Another generalization is

doi:10.1016/j.cam.2015.01.035
fatcat:zj3pgnd2v5gxteyfsiv3c25tzy
*Hermite*-*Padé**approximation*where a vector of Laurent series is*simultaneously**approximated*by a vector of rational*approximants*with a common denominator (Type II) or one tries ... Multiple orthogonal polynomials are related to*Hermite*-*Padé**approximation*. The type II polynomials appear in vectors that are*simultaneously*orthogonal to a vector of measures. ...
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