Download or read book Interpolation and Approximation of Sparse Multivariate Polynomials Over GF 2 written by International Business Machines Corporation. Research Division and published by . This book was released on 1990 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is shown that [formula] evaluation points are sufficient for the (deterministic) [epsilon]-approximation of any t-sparse function, and that an order of [formula] points are necessary for this purpose, where [alpha](t, [epsilon]) [greater than or equal to] 0.694 for a large range of t and [epsilon]. Similar bounds hold for the t-term DNF case as well. Finally, a probabilistic polynomial-time algorithm is presented for the [epsilon]-approximation of any t-sparse function."
Download or read book Effective Polynomial Computation written by Richard Zippel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: Effective Polynomial Computation is an introduction to the algorithms of computer algebra. It discusses the basic algorithms for manipulating polynomials including factoring polynomials. These algorithms are discussed from both a theoretical and practical perspective. Those cases where theoretically optimal algorithms are inappropriate are discussed and the practical alternatives are explained. Effective Polynomial Computation provides much of the mathematical motivation of the algorithms discussed to help the reader appreciate the mathematical mechanisms underlying the algorithms, and so that the algorithms will not appear to be constructed out of whole cloth. Preparatory to the discussion of algorithms for polynomials, the first third of this book discusses related issues in elementary number theory. These results are either used in later algorithms (e.g. the discussion of lattices and Diophantine approximation), or analogs of the number theoretic algorithms are used for polynomial problems (e.g. Euclidean algorithm and p-adic numbers). Among the unique features of Effective Polynomial Computation is the detailed material on greatest common divisor and factoring algorithms for sparse multivariate polynomials. In addition, both deterministic and probabilistic algorithms for irreducibility testing of polynomials are discussed.
Download or read book Learning Theory written by Hans Ulrich Simon and published by Springer. This book was released on 2006-09-29 with total page 667 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 19th Annual Conference on Learning Theory, COLT 2006, held in Pittsburgh, Pennsylvania, USA, June 2006. The book presents 43 revised full papers together with 2 articles on open problems and 3 invited lectures. The papers cover a wide range of topics including clustering, un- and semi-supervised learning, statistical learning theory, regularized learning and kernel methods, query learning and teaching, inductive inference, and more.
Download or read book LATIN 2022 Theoretical Informatics written by Armando Castañeda and published by Springer Nature. This book was released on 2022-10-28 with total page 782 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 15th Latin American Symposium on Theoretical Informatics, LATIN 2022, which took place in Guanajuato, Mexico, in November 2022. The 46 papers presented in this volume were carefully reviewed and selected from 114 submissions. They were organized in topical sections as follows: Algorithms and Data Structures; Approximation Algorithms; Cryptography; Social Choice Theory; Theoretical Machine Learning; Automata Theory and Formal Languages; Combinatorics and Graph Theory; Complexity Theory; Computational Geometry. Chapter “Klee’s Measure Problem Made Oblivious” is available open access under a CC BY 4.0 license.
Download or read book Automata Languages and Programming written by Luca Aceto and published by Springer Science & Business Media. This book was released on 2008-06-24 with total page 919 pages. Available in PDF, EPUB and Kindle. Book excerpt: ICALP 2008, the 35th edition of the International Colloquium on Automata, Languages and Programming, was held in Reykjavik, Iceland, July 7–11, 2008. ICALP is a series of annual conferences of the European Association for Th- reticalComputer Science(EATCS) which ?rsttook placein 1972.This year,the ICALP program consisted of the established Track A (focusing on algorithms, automata,complexityandgames)andTrackB(focusing onlogic,semanticsand theory of programming), and of the recently introduced Track C (focusing on security and cryptography foundations). In response to the call for papers, the Program Committees received 477 submissions, the highest ever: 269 for Track A, 122 for TrackB and 86 for Track C. Out of these, 126 papers were selected for inclusion in the scienti?c program: 70 papers for Track A, 32 for Track B and 24 for Track C. The selection was made by the Program Committees based on originality, quality, and relevance to theoretical computer science. The quality of the manuscripts was very high indeed, and many deserving papers could not be selected. ICALP 2008 consisted of ?ve invited lectures and the contributed papers.
Download or read book On zero testing and interpolation of k sparse multivariate polynomials over finite fields written by and published by . This book was released on 1988 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Algorithmic Learning Theory written by Klaus P. Jantke and published by Springer Science & Business Media. This book was released on 1993-10-20 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: Annotation This volume contains the papers that were presented at theThird Workshop onAlgorithmic Learning Theory, held in Tokyoin October 1992. In addition to 3invited papers, the volumecontains 19 papers accepted for presentation, selected from29 submitted extended abstracts. The ALT workshops have beenheld annually since 1990 and are organized and sponsored bythe Japanese Society for Artificial Intelligence. The mainobjective of these workshops is to provide an open forum fordiscussions and exchanges of ideasbetween researchers fromvarious backgrounds in this emerging, interdisciplinaryfield of learning theory. The volume is organized into partson learning via query, neural networks, inductive inference, analogical reasoning, and approximate learning.
Download or read book Property Testing written by Dana Ron and published by Now Publishers Inc. This book was released on 2008 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: This survey focuses on results for testing properties of functions that are of interest to the learning theory community.
Download or read book SIAM Journal on Computing written by Society for Industrial and Applied Mathematics and published by . This book was released on 1998 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Verification by Error Modeling written by Katarzyna Radecka and published by Springer Science & Business Media. This book was released on 2003-11-30 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the basis for reusing the test vector generation and simulation for the purpose of implementation verification, to result in a significant timesaving. It brings the results in the direction of merging manufacturing test vector generation and verification.
Download or read book Learning Theory written by John Shawe-Taylor and published by Springer. This book was released on 2004-06-11 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 17th Annual Conference on Learning Theory, COLT 2004, held in Banff, Canada in July 2004. The 46 revised full papers presented were carefully reviewed and selected from a total of 113 submissions. The papers are organized in topical sections on economics and game theory, online learning, inductive inference, probabilistic models, Boolean function learning, empirical processes, MDL, generalisation, clustering and distributed learning, boosting, kernels and probabilities, kernels and kernel matrices, and open problems.
Download or read book Multivariate Polynomial Approximation written by Manfred Reimer and published by Birkhäuser. This book was released on 2012-12-06 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces general theory by presenting the most important facts on multivariate interpolation, quadrature, orthogonal projections and their summation, all treated under a constructive view, and embedded in the theory of positive linear operators. On this background, the book builds the first comprehensive introduction to the theory of generalized hyperinterpolation. Several parts of the book are based on rotation principles, which are presented in the beginning of the book.
Download or read book Fast parallel algorithms for sparse multivariate polynomial interpolation over finite fields written by Dima J. Grigorʹev and published by . This book was released on 1988 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Proceedings of the Annual ACM Conference on Computational Learning Theory written by and published by . This book was released on 1995 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Interpolation and Approximation by Polynomials written by George M. Phillips and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: In addition to coverage of univariate interpolation and approximation, the text includes material on multivariate interpolation and multivariate numerical integration, a generalization of the Bernstein polynomials that has not previously appeared in book form, and a greater coverage of Peano kernel theory than is found in most textbooks. There are many worked examples and each section ends with a number of carefully selected problems that extend the student's understanding of the text. The author is well known for his clarity of writing and his many contributions as a researcher in approximation theory.
Download or read book Frontiers in Interpolation and Approximation written by N. K. Govil and published by CRC Press. This book was released on 2006-07-20 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dedicated to the well-respected research mathematician Ambikeshwar Sharma, Frontiers in Interpolation and Approximation explores approximation theory, interpolation theory, and classical analysis. Written by authoritative international mathematicians, this book presents many important results in classical analysis, wavelets, and interpolation theory. Some topics covered are Markov inequalities for multivariate polynomials, analogues of Chebyshev and Bernstein inequalities for multivariate polynomials, various measures of the smoothness of functions, and the equivalence of Hausdorff continuity and pointwise Hausdorff-Lipschitz continuity of a restricted center multifunction. The book also provides basic facts about interpolation, discussing classes of entire functions such as algebraic polynomials, trigonometric polynomials, and nonperiodic transcendental entire functions. Containing both original research and comprehensive surveys, this book provides researchers and graduate students with important results of interpolation and approximation.
Download or read book Sparse Polynomial Interpolation and the Fast Euclidean Algorithm written by Su Ko and published by . This book was released on 2012 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: We introduce an algorithm to interpolate sparse multivariate polynomials with integer coefficients. Our algorithm modifies Ben-Or and Tiwari's deterministic algorithm for interpolating over rings of characteristic zero to work modulo p, a smooth prime of our choice. We present benchmarks comparing our algorithm to Zippel's probabilistic sparse interpolation algorithm, demonstrating that our algorithm makes fewer probes for sparse polynomials. Our interpolation algorithm requires finding roots of a polynomial in GF(p)[x], which in turn requires an efficient polynomial GCD algorithm. Motivated by this observation, we review the Fast Extended Euclidean algorithm for univariate polynomials, which recursively computes the GCD using a divide-and-conquer approach. We present benchmarks for our implementation of the classical and fast versions of the Euclidean algorithm demonstrating a good speedup. We discuss computing resultants as an application of the fast GCD algorithm.
