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Algorithms for Simultaneous Padé Approximations
2016
Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation - ISSAC '16
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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 ...
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. ...
doi:10.1145/2930889.2930933
dblp:conf/issac/RosenkildeS16
fatcat:ew5jndxpovg2hijommcgiouuau
A uniform approach for Hermite Padé and simultaneous Padé approximants and their matrix-type generalizations
1992
Numerical Algorithms
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This includes descriptions of vector and matrix 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. ...
doi:10.1007/bf02141914
fatcat:5wyrxru4dndxtmhwhtfyb47rha
An A-stable Explicit Numerical Integration Method Based on Padé Approximation
2017
DEStech Transactions on Engineering and Technology Research
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By comparing the results of 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. ...
doi:10.12783/dtetr/iceea2016/6682
fatcat:7v44736dirc2pgvzix3idhtsdm
COMPARISON OF DIFFERENT ORDERS PADÉ FRACTIONAL ORDER PD05 CONTROL ALGORITHM IMPLEMENTATIONS
2006
IFAC Proceedings Volumes
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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. ...
doi:10.3182/20060719-3-pt-4902.00063
fatcat:c2hxhydpejfdvc4zgbrqrz5g7i
Page 1563 of Mathematical Reviews Vol. , Issue 93c
[page]
1993
Mathematical Reviews
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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
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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 ...
Page 6311 of Mathematical Reviews Vol. , Issue 98J
[page]
1998
Mathematical Reviews
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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. ...
Page 4108 of Mathematical Reviews Vol. , Issue 88h
[page]
1988
Mathematical Reviews
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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 ...
Fraction-free computation of simultaneous padé approximants
2009
Proceedings of the 2009 international symposium on Symbolic and algebraic computation - ISSAC '09
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How to Compute 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 ...
doi:10.1145/1576702.1576708
dblp:conf/issac/BeckermannL09
fatcat:k5laijlphzgmzibdo5ak3y2ip4
Computing the matrix sine and cosine simultaneously with a reduced number of products
2021
Applied Numerical Mathematics
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The resulting 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] . ...
doi:10.1016/j.apnum.2021.01.009
fatcat:ip6chleu4zci3foiescbqkjciq
Computing the matrix sine and cosine simultaneously with a reduced number of products
[article]
2020
arXiv
pre-print
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A new procedure is presented 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] . ...
arXiv:2010.00465v1
fatcat:wmsboutp7bd2jamp5vy4ka5wmy
Page 2995 of Mathematical Reviews Vol. , Issue 97E
[page]
1997
Mathematical Reviews
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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
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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].) ...
Page 4928 of Mathematical Reviews Vol. , Issue 97H
[page]
1997
Mathematical Reviews
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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. ...
Page 4456 of Mathematical Reviews Vol. , Issue 97G
[page]
1997
Mathematical Reviews
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Simultaneous Padé (SP) approximation is a dual problem. ...
and simultaneous Padé systems. ...
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