Download or read book A Zero test and an Interpolation Algorithm for the Shifted Sparse Polynomials written by Dima Grigorʹev and published by . This book was released on 1992 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Applied Algebra Algebraic Algorithms and Error Correcting Codes written by Gérard Cohen and published by Springer Science & Business Media. This book was released on 1993-04-20 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Researchers may find themselves confronted with proteases, either because they play an essential role in a particular process they are studying, or because they interfere with that process. In either case they may need to investigate or inhibit the proteolytic activity. Others may wish to use proteolytic enzymes as laboratory tools. This book has been written with these investigators in mind and includes assay methods using natural and artificial substrates, genetic-based assays, and strategies for the inhibition, purification and crystallization of proteases. In selected chapters the use of proteolytic enzymes to analyze proteins, segregate cells or in peptide synthesis is covered.
Download or read book Finite Fields Theory and Computation written by Igor Shparlinski and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is mainly devoted to some computational and algorithmic problems in finite fields such as, for example, polynomial factorization, finding irreducible and primitive polynomials, the distribution of these primitive polynomials and of primitive points on elliptic curves, constructing bases of various types and new applications of finite fields to other areas of mathematics. For completeness we in clude two special chapters on some recent advances and applications of the theory of congruences (optimal coefficients, congruential pseudo-random number gener ators, modular arithmetic, etc.) and computational number theory (primality testing, factoring integers, computation in algebraic number theory, etc.). The problems considered here have many applications in Computer Science, Cod ing Theory, Cryptography, Numerical Methods, and so on. There are a few books devoted to more general questions, but the results contained in this book have not till now been collected under one cover. In the present work the author has attempted to point out new links among different areas of the theory of finite fields. It contains many very important results which previously could be found only in widely scattered and hardly available conference proceedings and journals. In particular, we extensively review results which originally appeared only in Russian, and are not well known to mathematicians outside the former USSR.
Download or read book Automata Languages and Programming written by Javier Esparza and published by Springer. This book was released on 2014-06-11 with total page 1122 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume set of LNCS 8572 and LNCS 8573 constitutes the refereed proceedings of the 41st International Colloquium on Automata, Languages and Programming, ICALP 2014, held in Copenhagen, Denmark, in July 2014. The total of 136 revised full papers presented together with 4 invited talks were carefully reviewed and selected from 484 submissions. The papers are organized in three tracks focussing on Algorithms, Complexity, and Games, Logic, Semantics, Automata, and Theory of Programming, Foundations of Networked Computation.
Download or read book Computer Mathematics written by Ruyong Feng and published by Springer. This book was released on 2014-09-30 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers original research and the latest advances in symbolic, algebraic and geometric computation; computational methods for differential and difference equations, symbolic-numerical computation; mathematics software design and implementation; and scientific and engineering applications based on features, invited talks, special sessions and contributed papers presented at the 9th (in Fukuoka, Japan in 2009) and 10th (in Beijing China in 2012) Asian Symposium on Computer Mathematics (ASCM). Thirty selected and refereed articles in the book present the conference participants’ ideas and views on researching mathematics using computers.
Download or read book Proceedings of the International Symposium Symbolic and Algebraic Computation written by and published by . This book was released on 2002 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Early Termination Strategies in Sparse Interpolation Algorithms written by and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A black box polynomial is an object that takes as input a valuefor each variable and evaluates the polynomial at the given input. The process of determining the coefficients and terms of a blackbox polynomial is the problem of black box polynomialinterpolation. Two major approaches have been addressing suchpurpose: the dense algorithms whose computational complexities aresensitive to the degree of the target polynomial, and the sparsealgorithms that take advantage of the situation when the number ofnon-zero terms in a designate basis is small. In this dissertationwe cover power, Chebyshev, and Pochhammer term bases. However, asparse algorithm is less efficient when the target polynomial isdense, and both approaches require as input an upper bound oneither the degree or the number of non-zero terms. By introducingrandomization into existing algorithms, we demonstrate and developa probabilistic approach which we call 'early termination'. Inparticular we prove that with high probability of correctness theearly termination strategy makes different polynomialinterpolation algorithms 'smart' by adapting to the degree or tothe number of non-zero terms during the process when either is notsupplied as an input. Based on the early termination strategy, wedescribe new efficient univariate algorithms that race a denseagainst a sparse interpolation algorithm in order to exploit thesuperiority of one of them. We apply these racing algorithms asthe univariate interpolation procedure needed in Zippel's multivariate sparse interpolation method. We enhance the earlytermination approach with thresholds, and present insights toother such heuristic improvements. Some potential of the early termination strategy is observed for computing a sparse shift, where a polynomial becomes sparse through shifting the variables by a constant.
Download or read book An Interpolation Algorithm for Sparse Polynomials Over Zm written by Kai Werther and published by . This book was released on 1993 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Sparse Polynomial Interpolation and the Fast Euclidean Algorithm written by Soo Go 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.
Download or read book Mathematical Reviews written by and published by . This book was released on 2004 with total page 820 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Early Termination Strategies in Sparse Interpolation Algorithms written by Wen-shin Lee and published by . This book was released on 2001 with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt: Keywords: Sparse polynomial, Black box polynomial, Interpolation, Sparse interpolation, Randomized algorithm, Chebyshev basis, Pochhammer basis, Early termination, Racing two algorithms, Sparse shift, Zippel's algorithm, Ben-Or's and Tiwari's algorithm.
Download or read book ISSAC 96 written by Y. N. Lakshman and published by Association for Computing Machinery (ACM). This book was released on 1996 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Algorithms and Theory of Computation Handbook written by Mikhail J. Atallah and published by CRC Press. This book was released on 1998-11-23 with total page 1328 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algorithms and Theory of Computation Handbook is a comprehensive collection of algorithms and data structures that also covers many theoretical issues. It offers a balanced perspective that reflects the needs of practitioners, including emphasis on applications within discussions on theoretical issues. Chapters include information on finite precision issues as well as discussion of specific algorithms where algorithmic techniques are of special importance, including graph drawing, robotics, forming a VLSI chip, vision and image processing, data compression, and cryptography. The book also presents some advanced topics in combinatorial optimization and parallel/distributed computing. • applications areas where algorithms and data structuring techniques are of special importance • graph drawing • robot algorithms • VLSI layout • vision and image processing algorithms • scheduling • electronic cash • data compression • dynamic graph algorithms • on-line algorithms • multidimensional data structures • cryptography • advanced topics in combinatorial optimization and parallel/distributed computing
Download or read book Efficient Approximation Algorithms for Sparse Polynomials Over Finite Fields written by International Computer Science Institute and published by . This book was released on 1994 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "We obtain new lower bounds on the number of non zeros of sparse polynomials and give a fully polynomial time ([eta], [delta]) approximation algorithm for the number of non-zeros of multivariate sparse polynomials over a finite field of q elements and degree less than q - 1. This answers partially to an open problem of D. Grigoriev and M. Karpinski. Also, probabilistic and deterministic algorithms for testing identity to zero of a sparse polynomial given by a 'black-box' are given. Finally, we propose an algorithm to estimate the size of the image of a univariate sparse polynomial."
Download or read book Algebraic Complexity Theory written by Peter Bürgisser and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: The algorithmic solution of problems has always been one of the major concerns of mathematics. For a long time such solutions were based on an intuitive notion of algorithm. It is only in this century that metamathematical problems have led to the intensive search for a precise and sufficiently general formalization of the notions of computability and algorithm. In the 1930s, a number of quite different concepts for this purpose were pro posed, such as Turing machines, WHILE-programs, recursive functions, Markov algorithms, and Thue systems. All these concepts turned out to be equivalent, a fact summarized in Church's thesis, which says that the resulting definitions form an adequate formalization of the intuitive notion of computability. This had and continues to have an enormous effect. First of all, with these notions it has been possible to prove that various problems are algorithmically unsolvable. Among of group these undecidable problems are the halting problem, the word problem theory, the Post correspondence problem, and Hilbert's tenth problem. Secondly, concepts like Turing machines and WHILE-programs had a strong influence on the development of the first computers and programming languages. In the era of digital computers, the question of finding efficient solutions to algorithmically solvable problems has become increasingly important. In addition, the fact that some problems can be solved very efficiently, while others seem to defy all attempts to find an efficient solution, has called for a deeper under standing of the intrinsic computational difficulty of problems.
