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Fast computation of divided differences and parallel hermite interpolation

1989
*
Journal of Complexity
*

We present

doi:10.1016/0885-064x(89)90018-6
fatcat:lgz2lm44x5a47cvyuibrxgg6ui
*parallel**algorithms**for**fast**polynomial*interpolation. ... Unlike alternate approaches which use the Lagrange representation, the*algorithms*described in this paper are based on the*fast**parallel**evaluation*of a closed formula*for*the generalized divided differences ...*POLYNOMIAL**EVALUATION*As mentioned by Egecioglu et al. (1987a) , a*fast**algorithm**for*the interpolation would not be very useful unless an*algorithm*of comparable speed could be designed*for*the*evaluation*...##
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A parallel method for fast and practical high-order newton interpolation

1990
*
BIT Numerical Mathematics
*

We present

doi:10.1007/bf02017348
fatcat:orii44aerbedjdh3b4nn6wg4na
*parallel**algorithms**for*the computation and*evaluation*of interpolating*polynomials*. ... The*algorithms*use*parallel*prefix techniques*for*the calculation of divided differences in the Newton representation of the interpolating*polynomial*. ... The interpolating*polynomial*in its Newton form can be*evaluated*by means of a*fast**parallel**algorithm*having the same characteristics. ...##
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Dense Arithmetic over Finite Fields with the CUMODP Library
[chapter]

2014
*
Lecture Notes in Computer Science
*

CUMODP is a CUDA library

doi:10.1007/978-3-662-44199-2_108
fatcat:3zqkss6555aixjitkprv7vesfa
*for*exact computations with dense*polynomials*over finite fields. ...*Algorithms*combine FFT-based and plain arithmetic, while the implementation strategy emphasizes reducing*parallelism*overheads and optimizing hardware usage. ...*fast**algorithm*). ...##
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Engineering a Delegatable and Error-Tolerant Algorithm for Counting Small Subgraphs
[chapter]

2018
*
2018 Proceedings of the Twentieth Workshop on Algorithm Engineering and Experiments (ALENEX)
*

We engineer an open-source GPU implementation of a distributed

doi:10.1137/1.9781611975055.16
dblp:conf/alenex/Kaski18
fatcat:hlfxvpbb2zdmrlf4venyyhipim
*algorithm*design of Björklund and Kaski [PODC 2016] where (i) the execution of the*algorithm*can be delegated [Goldwasser, Kalai, and Rothblum ... Footnote 4*for*an analysis of the over-provisioning needed to tolerate adversarial errors. ... To expose sufficient*parallelism*in the design, we look inside the*evaluation**algorithm**for**parallelism*and implement both the preprocessing and the*fast*matrix multiplication steps using Yates's*algorithm*...##
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Some parallel methods for polynomial root-finding

1987
*
Journal of Computational and Applied Mathematics
*

Further places in

doi:10.1016/0377-0427(87)90056-2
fatcat:z46g2nz6grarbehb7blaepsady
*polynomial*root-finding*algorithms*where*parallel*behaviour can be introduced are described. ...*Parallelizations*of various different methods*for*determining the roots of a*polynomial*are discussed. These include methods which locate a single root only as well as those which find all roots. ... The quotient-difference*algorithm*tends to be*fast*as it does not have to perform*polynomial**evaluations*at each step. ...##
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Page 5714 of Mathematical Reviews Vol. , Issue 2000h
[page]

2000
*
Mathematical Reviews
*

Skrzipek, A Christoffel- Darboux-type formula

*for*Szegd*polynomials*and*polynomial**evaluation*(203-216); Kurt Suchy, Applications of tensor-valued tri-variate Hermite*polynomials*and spherical harmonics ...*parallel*recursive QR factoriza- tion*algorithms**for*SMP systems (120-128); Enric Fontdecaba Baig, José M. ...##
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Automatic Library Generation for Modular Polynomial Multiplication
[article]

2016
*
arXiv
*
pre-print

In this paper we design and implement

arXiv:1609.01010v1
fatcat:73syghptxja5tjb5ifmfomv7uu
*algorithms**for**polynomial*multiplication using approaches based the*fast*Fourier transform (FFT) and the truncated Fourier transform (TFT). ...*Polynomial*multiplication is a key*algorithm*underlying computer algebra systems (CAS) and its efficient implementation is crucial*for*the performance of CAS. ... Recently, [30] introduced*parallel**algorithms**for*sparse*polynomial*multiplication using heaps, and [11, 16] focused on sparse interpolation*for*multivariate*polynomial*and*for*over finite fields, ...##
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On the Parallelization of Subproduct Tree Techniques Targeting Many-Core Architectures
[chapter]

2014
*
Lecture Notes in Computer Science
*

the traditional

doi:10.1007/978-3-319-10515-4_13
fatcat:wnvxdha7hrbwxecz76npmh3bsq
*algorithms**for**polynomial**evaluation*and interpolation based on subproduct-tree trees, by introducing the notion of a subinverse tree. ... Contributions of this work Summary We propose*parallel**algorithms**for*performing subproduct tree construction,*evaluation*and interpolation and report on their implementation on many-core GPUs We enhance ...##
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On Speed versus Accuracy: Some Case Studies

1996
*
Journal of Complexity
*

More precisely, we focus on a set of significant examples and prove that: (1) the fastest known

doi:10.1006/jcom.1996.0016
fatcat:mss7vwdmivdlph7dcpphmfcegm
*polynomial**evaluation**algorithms*are not stable, (2) LUP decomposition cannot be computed stably in polylogarithmic ...*parallel*time, and (3) reductions among computational problems do not in general constitute a practical tool*for*solving numerical problems. ... The known O(n log 2 n) methods*for**polynomial**evaluation*at many points, which reduces to*fast**polynomial*multiplication and division, are not strongly stable. Proof. ...##
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A Parallel Algorithm to Evaluate Chebyshev Series on a Message Passing Environment

1998
*
SIAM Journal on Scientific Computing
*

A simple

doi:10.1137/s1064827596312857
fatcat:en3utck2xzhsbg2toymg62fm2y
*parallel**algorithm**for*the*evaluation*of*polynomials*written in the Chebyshev form is introduced. ... By this method only 2 ⌈log 2 (p − 2)⌉ + ⌈log 2 p⌉ + 4 ⌈N/p⌉ − 7 steps on p processors are needed to*evaluate*a Chebyshev series of degree N . ...*For*a general value N the*algorithm*is similar, but it requires small changes. First, we express the*evaluation*of the Chebyshev*polynomials*in*parallel*. ...##
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Error-Correcting and Verifiable Parallel Inference in Graphical Models

2020
*
PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE
*

We present a novel framework

doi:10.1609/aaai.v34i06.6580
fatcat:avzrzy2ctbavvdz2rj2bjvohpi
*for**parallel*exact inference in graphical models. ... Our main technical contribution amounts to designing a low-degree*polynomial*extension of the cutset approach, and then reducing to a univariate*polynomial*employing techniques recently developed*for*noninteractive ...*Fast**Algorithms**for*Univariate*Polynomials*. Let us recall the basic toolkit*for*computing with univariate*polynomials*(von zur Gathen and Gerhard 2013). ...##
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Parallel evaluation of Chebyshev and trigonometric series

1999
*
Computers and Mathematics with Applications
*

In this paper, we introduce a general

doi:10.1016/s0898-1221(99)00289-8
fatcat:2zldehdwejglhobvcq4ewngvqm
*parallel**algorithm**for*the*evaluation*of Chebyshev and trigonometric series. ... Several examples, carried out on a Cray T3D, are provided comparing the Forsythe and Clenshaw*parallel**algorithms*. (~) ... The plot,*for*each*polynomial*, has first a region of*fast*decrease, being the slope higher*for*low degree*polynomials*. ...##
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Page 3470 of Mathematical Reviews Vol. , Issue 94f
[page]

1994
*
Mathematical Reviews
*

This paper develops some new techniques in order to devise

*fast**parallel**algorithms**for*improved*parallel*computations, including the*evaluation*of Krylov sequences*for*Toeplitz-like and Hankel- like matrices ... The results can be further extended to such computational problems as*fast**parallel**evaluation*of rank T, of the null space of 7, of the minimum span of a linear recurrence sequence (Berlekamp-Massey problem ...##
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An Efficient Algorithm for Fast Computation of Pseudo-Zernike Moments

2003
*
International journal of pattern recognition and artificial intelligence
*

The

doi:10.1142/s0218001403002769
fatcat:7hefdi46r5bzholuktmv3lgs3e
*algorithm*consists of a two-stage recurrence relation*for*radial*polynomials*and coefficients of the*polynomials*, which are specifically derived*for**fast*computation of pseudo-Zernike moments. ... This paper discusses the drawbacks of the existing methods, and proposes an efficient recursive*algorithm*to compute the pseudo-Zernike moments. ... The*algorithm*comprises of two recurrence relations that are specifically derived*for*radial*polynomials*and coefficients of the*polynomials**for**fast*computation of pseudo-Zernike moments. ...##
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How proofs are prepared at Camelot
[article]

2016
*
arXiv
*
pre-print

Further results include novel

arXiv:1602.01295v1
fatcat:pqozv4nul5e7rakfbsra2al7pu
*algorithms**for*counting triangles in sparse graphs, computing the chromatic*polynomial*of a graph, and computing the Tutte*polynomial*of a graph. ... Complexity, Report TR16-002, January 2016] with the observation that Merlin's magic is not needed*for*batch*evaluation*---mere Knights can prepare the proof, in*parallel*, and with intrinsic error-correction ... Acknowledgments We thank Ryan Williams*for*useful discussions and giving us early access to his manuscript describing his batch*evaluation*framework [35] of which the present "Camelot" framework forms ...
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