Randomization Methods in Algorithm Design

Randomization Methods in Algorithm Design

Author: Panos M. Pardalos

Publisher: American Mathematical Soc.

Published: 1999

Total Pages: 335

ISBN-13: 0821809164

DOWNLOAD EBOOK

This volume is based on proceedings held during the DIMACS workshop on Randomization Methods in Algorithm Design in December 1997 at Princeton. The workshop was part of the DIMACS Special Year on Discrete Probability. It served as an interdisciplinary research workshop that brought together a mix of leading theorists, algorithmists and practitioners working in the theory and implementation aspects of algorithms involving randomization. Randomization has played an important role in the design of both sequential and parallel algorithms. The last decade has witnessed tremendous growth in the area of randomized algorithms. During this period, randomized algorithms went from being a tool in computational number theory to finding widespread applications in many problem domains. Major topics covered include randomization techniques for linear and integer programming problems, randomization in the design of approximate algorithms for combinatorial problems, randomization in parallel and distributed algorithms, practical implementation of randomized algorithms, de-randomization issues, and pseudo-random generators. This volume focuses on theory and implementation aspects of algorithms involving randomization. It would be suitable as a graduate or advanced graduate text.


Computation of Generalized Matrix Inverses and Applications

Computation of Generalized Matrix Inverses and Applications

Author: Ivan Stanimirović

Publisher: CRC Press

Published: 2017-12-14

Total Pages: 269

ISBN-13: 1351630059

DOWNLOAD EBOOK

This volume offers a gradual exposition to matrix theory as a subject of linear algebra. It presents both the theoretical results in generalized matrix inverses and the applications. The book is as self-contained as possible, assuming no prior knowledge of matrix theory and linear algebra. The book first addresses the basic definitions and concepts of an arbitrary generalized matrix inverse with special reference to the calculation of {i,j,...,k} inverse and the Moore–Penrose inverse. Then, the results of LDL* decomposition of the full rank polynomial matrix are introduced, along with numerical examples. Methods for calculating the Moore–Penrose’s inverse of rational matrix are presented, which are based on LDL* and QDR decompositions of the matrix. A method for calculating the A(2)T;S inverse using LDL* decomposition using methods is derived as well as the symbolic calculation of A(2)T;S inverses using QDR factorization. The text then offers several ways on how the introduced theoretical concepts can be applied in restoring blurred images and linear regression methods, along with the well-known application in linear systems. The book also explains how the computation of generalized inverses of matrices with constant values is performed. It covers several methods, such as methods based on full-rank factorization, Leverrier–Faddeev method, method of Zhukovski, and variations of the partitioning method.


Finite Fields: Theory and Computation

Finite Fields: Theory and Computation

Author: Igor Shparlinski

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 532

ISBN-13: 940159239X

DOWNLOAD EBOOK

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.


Computer Algebra Handbook

Computer Algebra Handbook

Author: Johannes Grabmeier

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 656

ISBN-13: 3642558267

DOWNLOAD EBOOK

This Handbook gives a comprehensive snapshot of a field at the intersection of mathematics and computer science with applications in physics, engineering and education. Reviews 67 software systems and offers 100 pages on applications in physics, mathematics, computer science, engineering chemistry and education.


Recent Advances in Parallel Virtual Machine and Message Passing Interface

Recent Advances in Parallel Virtual Machine and Message Passing Interface

Author: Jack Dongarra

Publisher: Springer Science & Business Media

Published: 2003-09-23

Total Pages: 712

ISBN-13: 3540201491

DOWNLOAD EBOOK

This book constitutes the refereed proceedings of the 10th European PVM/MPI Users' Group Meeting held in Venice, Italy, in September/October 2003. The 64 revised full papers and 16 revised short papers presented together with abstracts of 8 invited contributions and 7 reviewed special track papers were carefully reviewed and selected from 115 submissions. The papers are organized in topical sections on evaluation and performance analysis; parallel algorithms using message passing; extensions, improvements, and implementations of PVM/MPI; parallel programming tools; applications in science and engineering; grid and heterogeneous computing; and numerical simulation of parallel engineering environments - ParSim 2003.


EUROCAL '87

EUROCAL '87

Author: James H. Davenport

Publisher: Springer Science & Business Media

Published: 1989-08-09

Total Pages: 516

ISBN-13: 9783540515173

DOWNLOAD EBOOK

This is the sixth in a series of conference proceedings of international conferences on computer algebra held in Europe. All the preceding ones have also been published as Lecture Notes in Computer Science. They contain original research material not published elsewhere, and a few invited lectures summarising the state of the art. Computer algebra is the science of using computers to do algebraic calculations, rather than the purely arithmetic calculations which we all know computers can do. These calculations may be polynomial-like calculations - one thread of the conference was devoted to polynomial algorithms - or may relate to other areas of mathematics such as integration, the solution of differential equations, or geometry - a second thread was devoted to those topics. The calculations can be applied in a wide range of scientific and engineering subjects, and in branches of mathematics. Physics has benefitted especially from these calculations, and the proceedings contain many papers on this, and also papers on applications in computer aided design and robotics, to name but a few other applications. The third thread of the proceedings was devoted to these applications and to the computer algebra systems which perform these calculations.


Computer Algebra in Scientific Computing

Computer Algebra in Scientific Computing

Author: François Boulier

Publisher: Springer Nature

Published: 2023-08-23

Total Pages: 441

ISBN-13: 3031417240

DOWNLOAD EBOOK

This book constitutes the refereed proceedings of the 25th International Workshop on Computer Algebra in Scientific Computing, CASC 2023, which took place in Havana, Cuba, during August 28-September 1, 2023. The 22 full papers included in this book were carefully reviewed and selected from 29 submissions. They focus on the theory of symbolic computation and its implementation in computer algebra systems as well as all other areas of scientific computing with regard to their benefit from or use of computer algebra methods and software.


ISSAC '97

ISSAC '97

Author: W. W. (ed.) Küchlin

Publisher: Association for Computing Machinery (ACM)

Published: 1997

Total Pages: 450

ISBN-13:

DOWNLOAD EBOOK

This volume contains the fifty-nine research papers presented at the 1997 International Symposium on Symbolic and Algebraic Computation. The Symposium was held in Wailea on the island of Maui, Hawaii, USA, July 21-23, 1997 under the sponsorship of the ACM Special Interest Group in Symbolic and Algebraic Manipulation (SIGSAM) and the Special Interest Group on Numerical Mathematics (SIGNUM). The fifty-nine papers contained in this volume together with the two invited talks at the Symposium represent original research in all areas of symbolic and algebraic computation.


42nd Annual Symposium on Foundations of Computer Science

42nd Annual Symposium on Foundations of Computer Science

Author:

Publisher:

Published: 2001

Total Pages: 698

ISBN-13: 9780769513904

DOWNLOAD EBOOK

Proceedings of the October 2001 symposium. Three tutorial sessions discuss game theory and mathematical economics a theoretical computer scientist's introduction; algorithmic applications of low-distortions geometric embeddings; and coding theory. About 60 additional papers address related topics. L