Download or read book Error Free Polynomial Matrix Computations written by E.V. Krishnamurthy and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is written as an introduction to polynomial matrix computa tions. It is a companion volume to an earlier book on Methods and Applications of Error-Free Computation by R. T. Gregory and myself, published by Springer-Verlag, New York, 1984. This book is intended for seniors and graduate students in computer and system sciences, and mathematics, and for researchers in the fields of computer science, numerical analysis, systems theory, and computer algebra. Chapter I introduces the basic concepts of abstract algebra, including power series and polynomials. This chapter is essentially meant for bridging the gap between the abstract algebra and polynomial matrix computations. Chapter II is concerned with the evaluation and interpolation of polynomials. The use of these techniques for exact inversion of poly nomial matrices is explained in the light of currently available error-free computation methods. In Chapter III, the principles and practice of Fourier evaluation and interpolation are described. In particular, the application of error-free discrete Fourier transforms for polynomial matrix computations is consi dered.

Download or read book Polynomial and Matrix Computations written by Dario Bini and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our Subjects and Objectives. This book is about algebraic and symbolic computation and numerical computing (with matrices and polynomials). It greatly extends the study of these topics presented in the celebrated books of the seventies, [AHU] and [BM] (these topics have been under-represented in [CLR], which is a highly successful extension and updating of [AHU] otherwise). Compared to [AHU] and [BM] our volume adds extensive material on parallel com putations with general matrices and polynomials, on the bit-complexity of arithmetic computations (including some recent techniques of data compres sion and the study of numerical approximation properties of polynomial and matrix algorithms), and on computations with Toeplitz matrices and other dense structured matrices. The latter subject should attract people working in numerous areas of application (in particular, coding, signal processing, control, algebraic computing and partial differential equations). The au thors' teaching experience at the Graduate Center of the City University of New York and at the University of Pisa suggests that the book may serve as a text for advanced graduate students in mathematics and computer science who have some knowledge of algorithm design and wish to enter the exciting area of algebraic and numerical computing. The potential readership may also include algorithm and software designers and researchers specializing in the design and analysis of algorithms, computational complexity, alge braic and symbolic computing, and numerical computation.

Download or read book Methods and Applications of Error Free Computation written by R. T. Gregory and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is written as an introduction to the theory of error-free computation. In addition, we include several chapters that illustrate how error-free com putation can be applied in practice. The book is intended for seniors and first year graduate students in fields of study involving scientific computation using digital computers, and for researchers (in those same fields) who wish to obtain an introduction to the subject. We are motivated by the fact that there are large classes of ill-conditioned problems, and there are numerically unstable algorithms, and in either or both of these situations we cannot tolerate rounding errors during the numerical computations involved in obtaining solutions to the problems. Thus, it is important to study finite number systems for digital computers which have the property that computation can be performed free of rounding errors. In Chapter I we discuss single-modulus and multiple-modulus residue number systems and arithmetic in these systems, where the operands may be either integers or rational numbers. In Chapter II we discuss finite-segment p-adic number systems and their relationship to the p-adic numbers of Hensel [1908]. Each rational number in a certain finite set is assigned a unique Hensel code and arithmetic operations using Hensel codes as operands is mathe matically equivalent to those same arithmetic operations using the cor responding rational numbers as operands. Finite-segment p-adic arithmetic shares with residue arithmetic the property that it is free of rounding errors.

Download or read book Parallel Computation written by Jens Volkert and published by Springer Science & Business Media. This book was released on 1993-09-27 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Austrian Center for Parallel Computation (ACPC) is a cooperative research organization founded in 1989 to promote research and education in the field of software for parallel computer systems. The areas in which the ACPC is active include algorithms, languages, compilers, programming environments, and applications for parallel and high-performance computing systems. This volume contains the proceedings of the Second International Conference of the ACPC, held in Gmunden, Austria, October 1993. Authors from 17 countries submitted 44 papers, of which 15 were selected for inclusion in this volume, which also includes 4 invited papers by distinguished researchers. The volume is organized into parts on architectures (2 papers), algorithms (7 papers), languages (6 papers), and programming environments (4 papers).

Download or read book Advances in the Design of Symbolic Computation Systems written by Alfonso Miola and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: New methodological aspects related to design and implementation of symbolic computation systems are considered in this volume aiming at integrating such aspects into a homogeneous software environment for scientific computation. The proposed methodology is based on a combination of different techniques: algebraic specification through modular approach and completion algorithms, approximated and exact algebraic computing methods, object-oriented programming paradigm, automated theorem proving through methods à la Hilbert and methods of natural deduction. In particular the proposed treatment of mathematical objects, via techniques for method abstraction, structures classification, and exact representation, the programming methodology which supports the design and implementation issues, and reasoning capabilities supported by the whole framework are described.

Download or read book Algorithms and Theory of Computation Handbook 2 Volume Set written by Mikhail J. Atallah and published by CRC Press. This book was released on 2022-05-29 with total page 1904 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algorithms and Theory of Computation Handbook, Second Edition in a two volume set, provides an up-to-date compendium of fundamental computer science topics and techniques. It also illustrates how the topics and techniques come together to deliver efficient solutions to important practical problems. New to the Second Edition: Along with updating and revising many of the existing chapters, this second edition contains more than 20 new chapters. This edition now covers external memory, parameterized, self-stabilizing, and pricing algorithms as well as the theories of algorithmic coding, privacy and anonymity, databases, computational games, and communication networks. It also discusses computational topology, computational number theory, natural language processing, and grid computing and explores applications in intensity-modulated radiation therapy, voting, DNA research, systems biology, and financial derivatives. This best-selling handbook continues to help computer professionals and engineers find significant information on various algorithmic topics. The expert contributors clearly define the terminology, present basic results and techniques, and offer a number of current references to the in-depth literature. They also provide a glimpse of the major research issues concerning the relevant topics

Download or read book Mathematical System Theory written by Athanasios C. Antoulas and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the past three decades R.E. Kalman has been one of the most influential personalities in system and control theory. His ideas have been instrumental in a variety of areas. This is a Festschrift honoring his 60th birthday. It contains contributions from leading researchers in the field giving an account of the profound influence of his ideas in a number of areas of active research in system and control theory. For example, since their introduction by Kalman in the early 60's, the concepts of controllability and observability of dynamical systems with inputs, have been the corner stone of the great majority of investigations in the field.

Download or read book Computational Science ICCS 2003 written by Peter M.A. Sloot and published by Springer. This book was released on 2003-08-03 with total page 1188 pages. Available in PDF, EPUB and Kindle. Book excerpt: The four-volume set LNCS 2657, LNCS 2658, LNCS 2659, and LNCS 2660 constitutes the refereed proceedings of the Third International Conference on Computational Science, ICCS 2003, held concurrently in Melbourne, Australia and in St. Petersburg, Russia in June 2003. The four volumes present more than 460 reviewed contributed and invited papers and span the whole range of computational science, from foundational issues in computer science and algorithmic mathematics to advanced applications in virtually all application fields making use of computational techniques. These proceedings give a unique account of recent results in the field.

Download or read book Algorithms and Theory of Computation Handbook Volume 1 written by Mikhail J. Atallah and published by CRC Press. This book was released on 2009-11-20 with total page 974 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algorithms and Theory of Computation Handbook, Second Edition: General Concepts and Techniques provides an up-to-date compendium of fundamental computer science topics and techniques. It also illustrates how the topics and techniques come together to deliver efficient solutions to important practical problems. Along with updating and revising many

Download or read book Structured Matrices and Polynomials written by Victor Y. Pan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: This user-friendly, engaging textbook makes the material accessible to graduate students and new researchers who wish to study the rapidly exploding area of computations with structured matrices and polynomials. The book goes beyond research frontiers and, apart from very recent research articles, includes previously unpublished results.

Download or read book Algebraic Cryptanalysis written by Gregory Bard and published by Springer Science & Business Media. This book was released on 2009-08-14 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic Cryptanalysis bridges the gap between a course in cryptography, and being able to read the cryptanalytic literature. This book is divided into three parts: Part One covers the process of turning a cipher into a system of equations; Part Two covers finite field linear algebra; Part Three covers the solution of Polynomial Systems of Equations, with a survey of the methods used in practice, including SAT-solvers and the methods of Nicolas Courtois. Topics include: Analytic Combinatorics, and its application to cryptanalysis The equicomplexity of linear algebra operations Graph coloring Factoring integers via the quadratic sieve, with its applications to the cryptanalysis of RSA Algebraic Cryptanalysis is designed for advanced-level students in computer science and mathematics as a secondary text or reference book for self-guided study. This book is suitable for researchers in Applied Abstract Algebra or Algebraic Geometry who wish to find more applied topics or practitioners working for security and communications companies.

Download or read book Applied Cryptography and Network Security written by Mehdi Tibouchi and published by Springer Nature. This book was released on 2023-05-28 with total page 762 pages. Available in PDF, EPUB and Kindle. Book excerpt: The LNCS two-volume set 13905 and LNCS 13906 constitutes the refereed proceedings of the 21st International Conference on Applied Cryptography and Network Security, ACNS 2023, held in Tokyo, Japan, during June 19-22, 2023. The 53 full papers included in these proceedings were carefully reviewed and selected from a total of 263 submissions. They are organized in topical sections as follows: Part I: side-channel and fault attacks; symmetric cryptanalysis; web security; elliptic curves and pairings; homomorphic cryptography; machine learning; and lattices and codes. Part II: embedded security; privacy-preserving protocols; isogeny-based cryptography; encryption; advanced primitives; multiparty computation; and Blockchain.

Download or read book Handbook of Matrices written by Helmut Lütkepohl and published by John Wiley & Sons. This book was released on 1997-03-06 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matrices are used in many fields such as statistics, econometrics, mathematics, natural sciences and engineering. They provide a concise, simple method for describing long and complicated computations. This is a comprehensive handbook and dictionary of terms for matrix theory.

Download or read book Numerical And Symbolic Computations Of Generalized Inverses written by Yimin Wei and published by World Scientific. This book was released on 2018-07-18 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: We introduce new methods connecting numerics and symbolic computations, i.e., both the direct and iterative methods as well as the symbolic method for computing the generalized inverses. These will be useful for Engineers and Statisticians, in addition to applied mathematicians.Also, main applications of generalized inverses will be presented. Symbolic method covered in our book but not discussed in other book, which is important for numerical-symbolic computations.

Download or read book Mathematical Foundations of Computer Science written by Peter A. Fejer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Foundations of Computer Science, Volume I is the first of two volumes presenting topics from mathematics (mostly discrete mathematics) which have proven relevant and useful to computer science. This volume treats basic topics, mostly of a set-theoretical nature (sets, functions and relations, partially ordered sets, induction, enumerability, and diagonalization) and illustrates the usefulness of mathematical ideas by presenting applications to computer science. Readers will find useful applications in algorithms, databases, semantics of programming languages, formal languages, theory of computation, and program verification. The material is treated in a straightforward, systematic, and rigorous manner. The volume is organized by mathematical area, making the material easily accessible to the upper-undergraduate students in mathematics as well as in computer science and each chapter contains a large number of exercises. The volume can be used as a textbook, but it will also be useful to researchers and professionals who want a thorough presentation of the mathematical tools they need in a single source. In addition, the book can be used effectively as supplementary reading material in computer science courses, particularly those courses which involve the semantics of programming languages, formal languages and automata, and logic programming.

Download or read book Computational Geometry written by Franco P. Preparata and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "This book offers a coherent treatment, at the graduate textbook level, of the field that has come to be known in the last decade or so as computational geometry. ... ... The book is well organized and lucidly written; a timely contribution by two founders of the field. It clearly demonstrates that computational geometry in the plane is now a fairly well-understood branch of computer science and mathematics. It also points the way to the solution of the more challenging problems in dimensions higher than two." #Mathematical Reviews#1 "... This remarkable book is a comprehensive and systematic study on research results obtained especially in the last ten years. The very clear presentation concentrates on basic ideas, fundamental combinatorial structures, and crucial algorithmic techniques. The plenty of results is clever organized following these guidelines and within the framework of some detailed case studies. A large number of figures and examples also aid the understanding of the material. Therefore, it can be highly recommended as an early graduate text but it should prove also to be essential to researchers and professionals in applied fields of computer-aided design, computer graphics, and robotics." #Biometrical Journal#2

Download or read book Prototyping Oriented Software Development written by Walter R. Bischofberger and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for anyone who plans, designs and implements software systems, for anyone who is involved with quality assurance, and hence for anyone who is interested in the practicability of modern concepts, methods and tools in the software development process. The book aims at software engineers and at students with specialized interests in the area of software engineering. The reader is expected to be familiar with the fundamental concepts of software engineering. In writing the book, the authors tap years of experience in industrial projects and research work in the development of methods and tools that support the software development process. Perhaps now more than ever, the buzzword "software crisis" serves to alert us that software systems are often error-prone, that significant diffi culties arise in mastering complexity in the production of software systems, and that the acceptance and adequacy of software products is significantly lower than is the case with other technical products. The following goals have been suggested for the improvement of the software development process: • exact fulfillment of user requirements • increased reliability and robustness • greater modularity of both the development process and the product • simple and adequate operation, i. e. , better ergonomics • easy maintainability and extensibility • cost-effective portability • increased reusability of software components • reduced costs for production, operation and maintenance VI Preface Research and development work in the area of software engineering has in creased dramatically in recent years.