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Stochastic Discrete Clenshaw-Curtis Quadrature

2016
*
International Conference on Machine Learning
*

We propose an

dblp:conf/icml/PiatkowskiM16
fatcat:ilfth6gswjdjxawr74hvn4q6b4
*approximation*scheme that,*for*any discrete graphical model whose parameter vector has*bounded*norm, estimates the partition function with arbitrarily small error. ... Our algorithm relies on a near minimax optimal*polynomial**approximation*to the potential function and a Clenshaw-Curtis style quadrature. ... Acknowledgments This work has been supported*by*the Deutsche Forschungsgemeinschaft (DFG) within the collaborative research center SFB 876, project A1. ...##
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Page 8845 of Mathematical Reviews Vol. , Issue 2000m
[page]

2000
*
Mathematical Reviews
*

This basis has several useful properties— local minimal support,

*low**degree*of*polynomials*. ... We also present several problems that arise in*lower*-*degree**polynomials*.” 2000m:65021 65D15 41A30 Kushpel, A. K. ...##
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Effective approximation of the solutions of algebraic equations
[article]

2020
*
arXiv
*
pre-print

Let F be a holomorphic map whose components satisfy some

arXiv:1603.07298v2
fatcat:t5dzhucl7vb6bnpemnztrnyiqu
*polynomial*relations. We present an algorithm*for*constructing Nash maps locally*approximating*F, whose components satisfy the same relations. ...*For*i = m + 1, . . . , m + s, the*degree*of P ν i in z i is*bounded**by*the cardinality of the generic fiber in V*over*C m . ...*Bound**for*the*degree*of output*polynomials*We prove the claim: there is a*bound**for*the*degree*of P ν i in z i , i = 1, . . . ,m, independent of ν. ...##
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Reed-Muller Codes: Theory and Algorithms
[article]

2020
*
arXiv
*
pre-print

weight codewords using

arXiv:2002.03317v2
fatcat:oaeaq4yyhvdcth3g4djndgfypq
*lower**degree**polynomials*. ... In particular, the paper discusses the recent connections established between RM codes, thresholds of Boolean functions, polarization theory, hypercontractivity, and the techniques of*approximating**low*... We first show that each*polynomial*of weight at most β can be*approximated**by*an explicit function of some*lower*order derivatives. ...##
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Algebraic complexities and algebraic curves over finite fields

1987
*
Proceedings of the National Academy of Sciences of the United States of America
*

We prove

doi:10.1073/pnas.84.7.1739
pmid:16593816
pmcid:PMC304516
fatcat:bjn6jpkwhze45keyvqsjtdkf4e
*lower*and upper*bounds*on minimal complexities*over*finite fields, both linear in the number of inputs, using the relationship with linear coding theory and algebraic curves*over*finite fields ...*For*infinite fields minimal complexities are known [Winograd, S. (1977) Math. Syst. Theory 10, 169-180]. ... on ,lF(n, m) of multiplicative complexity*over*Fq of multiplication of a*polynomial*of*degree*n -1*by*a*polynomial*of*degree*m -1*for*q = 2: pFq(n, m) 2 max{N(n, m), N(m, n)} ...##
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Finding orthogonal vectors in discrete structures
[chapter]

2013
*
Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms
*

Letting HOPCROFT R denote Hopcroft's problem

doi:10.1137/1.9781611973402.135
dblp:conf/soda/WilliamsY14
fatcat:qucl3dve3vhjxlralylbh7xupy
*over*a ring R, we give randomized algorithms and almost matching*lower**bounds*(modulo a breakthrough in SAT algorithms)*for*HOPCROFT R , when R is the ring ... The algorithms arise from studying the communication problem of determining whether two lists of vectors (one list held*by*Alice, one*by*Bob) contain an orthogonal pair of vectors*over*a discrete structure ... Just as studying Z m*for*non-prime-power m was the key to developing subexponential locally decodable codes, studying Hopcroft's problem*over*Z m may lead to faster SAT algorithms. ...##
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A Novel Root-Finding Algorithm with Engineering Applications and Its Dynamics Via Computer Technology

2022
*
IEEE Access
*

We consider various different-

doi:10.1109/access.2022.3150775
fatcat:t7ovazqedzf6bdfnzms2xopjfq
*degrees*complex*polynomials**for*the graphical analysis and used a computer tool to create the polynomiographs of the proposed quartic-order algorithm and compare it to other ... We develop this algorithm*by*utilizing the forward-and finite-difference schemes on well-known Househ"older's method, resulting in an efficient and derivative-free algorithm with a*low*per iteration computing ...*for*the quadratic-*degree**polynomial*z 2 − 1 having two distinct roots: 1 and −1. ...##
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Lower Bounds for Constant Query Affine-Invariant LCCs and LTCs

2017
*
ACM Transactions on Computation Theory
*

This then allows us to

doi:10.1145/3016802
fatcat:s5tvj25yqzhsnpv2icij2rhrlu
*bound*the number of codewords, using known decomposition theorems which*approximate*any*bounded*function in terms of a finite number of*low*-*degree*non-classical*polynomials*, upto ... In this work, we give*lower**bounds*on the length of locally correctable and locally testable affine-invariant codes with constant query complexity. ... We thank Madhu Sudan*for*helpful pointers to previous work. The second author would like to thank his advisor, Zeev Dvir,*for*his guidance and encouragement. ...##
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Orthogonal Fourier–Mellin moments for invariant pattern recognition

1994
*
Optical Society of America. Journal A: Optics, Image Science, and Vision
*

*For*small images, the description

*by*the orthogonal Fourier-Mellin moments is better than that

*by*the Zernike moments in terms of image-reconstruction errors and signal-to-noise ratio. ... The new orthogonal radial

*polynomials*have more zeros than do the Zernike radial

*polynomials*in the region of small radial distance. ... and If(r, 0)12 are integrable and the

*polynomials*Qn(r) are

*bounded*

*over*(0,1) as n becomes infinite. 8 These conditions are, in general, satisfied. ...

##
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Improved Bounds on the Sign-Rank of AC^0

2016
*
International Colloquium on Automata, Languages and Programming
*

Specifically, they exhibited a matrix A = [F (x, y)] x,y

doi:10.4230/lipics.icalp.2016.37
dblp:conf/icalp/BunT16
fatcat:jhf5tpfjmbfkllrbxqh5nkgcmi
*for*a specific function We prove a generalization of Razborov and Sherstov's result, yielding exponential sign-rank*lower**bounds**for*a non-trivial ... class of functions (that includes the function used*by*Razborov and Sherstov). ... This can be viewed as a dual formulation of a*bound*on the growth of*low*-*degree**polynomials*. ...##
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Gravitational recoil from binary black hole mergers: The close-limit approximation

2006
*
Physical Review D
*

This is a

doi:10.1103/physrevd.74.124010
fatcat:fileqqackza7lbcaegtkhuo7y4
*lower**bound*because it neglects the initial merger phase. We can however obtain a rough estimate*by*using PN methods or the close-limit*approximation*. ... We also provide non-linear fits to these estimated upper and*lower**bounds*. ... Acknowledgments The authors acknowledge the support of the Center*for*Gravitational Wave Physics funded*by*the National Science Foundation under Cooperative Agreement PHY-0114375. ...##
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Homomorphic fingerprints under misalignments

2013
*
Proceedings of the 45th annual ACM symposium on Symposium on theory of computing - STOC '13
*

This

doi:10.1145/2488608.2488726
dblp:conf/stoc/AndoniGMP13
fatcat:my6bdailrre4hfzhj2ksvoukdm
*lower**bound*addresses a long-standing open problem on the*low*distor- * ... Fingerprinting is a widely-used technique*for*efficiently verifying that two files are identical. ... The authors would like to thank Robi Krauthgamer, Hossein Jowhari, and Atri Rudra*for*early conversations about the problem, as well as the anonymous referees*for*their valueable comments. ...##
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10.1162/153244302760200650

2000
*
Applied Physics Letters
*

We define a measure of complexity

doi:10.1162/153244302760200650
fatcat:yfeyp2m3pjb2dbuyu5m4dnm3zy
*for*data dependent hypothesis classes and provide data dependent versions of*bounds*on error deviance and estimation error. ... We also provide a structural risk minimization procedure*over*data dependent hierarchies and prove consistency. ... Acknowledgments We would like to thank Leonid Gurvits*for*a very helpful conversation. Clint Scovel gratefully acknowledges support from the Los Alamos DOE Program in Applied Mathematics. ...##
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On the Complexity of Familiar Functions and Numbers

1988
*
SIAM Review
*

This paper examines

doi:10.1137/1030134
fatcat:dyuvva7n6ffhrf7w6fr5pipvbi
*low*-complexity*approximations*to familiar functions and numbers. ...*For*most functions, provably optimal methods are not known; however the gap between what is known and what is possible is often small. ... The subscript on the order symbol is*for*emphasis. We will sometimes use 2 and rat as the*lower**bound*order symbols. ...##
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Bayesian Kernel Shaping for Learning Control

2008
*
Neural Information Processing Systems
*

It can be used

dblp:conf/nips/TingKVS08
fatcat:qxnrz6fv7ncqdkvsmzr7bcrtt4
*for*nonparametric regression with local*polynomials*or as a novel method to achieve nonstationary regression with Gaussian processes. ... We introduce a Bayesian formulation of nonparametric regression that, with the help of variational*approximations*, results in an EM-like algorithm*for*simultaneous estimation of regression and kernel parameters ... In this paper, we consider local kernel shaping*by*averaging*over*data samples with the help of locally*polynomial*models and formulate this approach, in a Bayesian framework,*for*both function*approximation*...
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