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

1992
*
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*. ... We show that this generalized form provides a uniform approach*for*different concepts of matrix-type*Padé**approximants*. ... example, to derive*algorithms*where both types of*approximants*are computed*simultaneously*. ...##
###
An A-stable Explicit Numerical Integration Method Based on Padé Approximation

2017
*
DEStech Transactions on Engineering and Technology Research
*

By comparing the results of

doi:10.12783/dtetr/iceea2016/6682
fatcat:7v44736dirc2pgvzix3idhtsdm
*Padé**approximation*method with the results of Taylor series expansion method, it proves that the Numerical integration method based on*Padé**approximation*has high accuracy. ... -node calculation system*for*simulation calculation. ... Thus, the*Padé**approximation*method is more suitable*for*numerical calculation of transient stability. ...##
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COMPARISON OF DIFFERENT ORDERS PADÉ FRACTIONAL ORDER PD05 CONTROL ALGORITHM IMPLEMENTATIONS

2006
*
IFAC Proceedings Volumes
*

*For*simulation purposes the robot prescribed motion is characterized through several locomotion variables and

*for*the walking performance evaluation are used two indices, one based on the mean absolute ... A set of simulation experiments reveals the influence of the different order

*Padé*PD 0.5 controllers tuning upon the proposed indices. ... Therefore, and considering all the previous results, we may state that the best order

*for*the

*Padé*

*approximation*when computing the G c1 (s)

*algorithm*yields

*for*u 4. ...

##
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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. ...##
###
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 6311 of Mathematical Reviews Vol. , Issue 98J
[page]

1998
*
Mathematical Reviews
*

Gutknecht [BIT 36 (1996), no. 2, 264-285; MR 97m:65085], we introduced a new look- ahead

*algorithm**for*recursively computing*Padé**approximants*. ... This*algorithm*generates a subsequence of the*Padé**approximants*on two adjacent rows (defined by fixed numerator degree) of the*Padé*table. ...##
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Page 4108 of Mathematical Reviews Vol. , Issue 88h
[page]

1988
*
Mathematical Reviews
*

Asymptotic behavior of linear forms

*for**simultaneous**Padé**approximants*. (Russian) Izv. Vyssh. Uchebn. Zaved. Mat. 1986, no. 2, 33-41, 84. ... Summary (translated from the Russian): “We prove the existence of asymptotic behavior of an nth degree root*for*a sequence of linear forms of*simultaneous**Padé**approximants**for*a class of systems of functions ...##
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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 ...*Simultaneous**Padé**Approximants*Given power series A 1 (z), . . . , A m (z) and integer N Find polynomials U 1 (z), ..., U m (z) and V (z) with : V (z)[A 1 (z), . . . , A m (z)] ≡ [U 1 (z), . . . , U m ...##
###
Computing the matrix sine and cosine simultaneously with a reduced number of products

2021
*
Applied Numerical Mathematics
*

The resulting

doi:10.1016/j.apnum.2021.01.009
fatcat:ip6chleu4zci3foiescbqkjciq
*algorithms*are more efficient than schemes based on*Padé**approximations**for*a wide range of norm matrices. ... A new procedure is presented*for*computing the matrix cosine and sine*simultaneously*by means of Taylor polynomial*approximations*. ... floating-point arithmetic, u ≤ 2 −53 ,*for*the new Taylor*algorithms*T c 2m , T s 2m+1 and*Padé**approximations*cm, sm [1] . ...##
###
Computing the matrix sine and cosine simultaneously with a reduced number of products
[article]

2020
*
arXiv
*
pre-print

A new procedure is presented

arXiv:2010.00465v1
fatcat:wmsboutp7bd2jamp5vy4ka5wmy
*for*computing the matrix cosine and sine*simultaneously*by means of Taylor polynomial*approximations*. ... The resulting*algorithms*are more efficient than schemes based on Pad\'e*approximations**for*a wide range of norm matrices. ... floating-point arithmetic, u ≤ 2 −53 ,*for*the new Taylor*algorithms*T c 2m , T s 2m+1 and*Padé**approximations*cm, sm [1] . ...##
###
Page 2995 of Mathematical Reviews Vol. , Issue 97E
[page]

1997
*
Mathematical Reviews
*

The main results in this paper are error formulas, conditions

*for*locally uniform convergence of the general order multivariate*Padé*-type*approximants*, and also conditions*for*geometric conver- gence. ... Summary: “*Simultaneous*rational*approximants*(SRA) to a pair of Markov functions (f;, f2) that forms a Nikishin system are investigated. ...##
###
Page 5753 of Mathematical Reviews Vol. , Issue 94j
[page]

1994
*
Mathematical Reviews
*

*For*41

*APPROXIMATIONS*AND EXPANSIONS 94j:-41016 \q| < 1 the authors prove convergence

*for*diagonal sequences of

*Padé*

*approximants*. ... The best

*simultaneous*uniform

*approximation*on RS-sets is stud- ied. (

*For*the definition of RS-sets, please see a paper by D. Amir [J. Approx. Theory 40 (1984), no. 3, 196-201; MR 85f:41031].) ...

##
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Page 4928 of Mathematical Reviews Vol. , Issue 97H
[page]

1997
*
Mathematical Reviews
*

*Padé*-type

*approximation*. ... The

*simultaneous*

*approximation*of a function and its derivatives is discussed and an estimate of the degree

*for*such an

*approximation*is given. ...

##
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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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