Download or read book Computer Arithmetic and Self Validating Numerical Methods written by Christian Ullrich and published by Academic Press. This book was released on 2014-05-10 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Notes and Reports in Mathematics in Science and Engineering, Volume VII: Computer Arithmetic and Self-Validating Numerical Methods compiles papers presented at the first international conference on “Computer Arithmetic and Self-Validating Numerical Methods, held in Basel from October 2 to 6, 1989. This book begins by providing a tutorial introduction to computer arithmetic with operations of maximum accuracy, differentiation arithmetic and enclosure methods, and programming languages for self-validating numerical methods. The rest of the chapters discuss the determination of guaranteed bounds for eigenvalues by variational methods and guaranteed inclusion of solutions of differential equations. An appendix covering the IMACS-GAMM resolution on computer arithmetic is provided at the end of this publication. This volume is recommended for researchers and professionals working on computer arithmetic and self-validating numerical methods.
Download or read book Contribution to Computer Arithmetic and Self validating Numerical Methods written by Christian Ullrich and published by . This book was released on 1990 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Contributions to Computer Arithmetic and Self validating Numerical Methods written by Christian Ullrich and published by . This book was released on 1990 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.
Download or read book Contributions to Computer Arithmetic and Self validating Numerical Methods written by Christian Ullrich and published by . This book was released on 1993 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Self Validating Numerics for Function Space Problems written by Edgar W. Kaucher and published by Elsevier. This book was released on 2014-06-20 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: Self-Validating Numerics for Function Space Problems describes the development of computational methods for solving function space problems, including differential, integral, and function equations. This seven-chapter text highlights three approaches, namely, the E-methods, ultra-arithmetic, and computer arithmetic. After a brief overview of the different self-validating approaches, this book goes on introducing the mathematical preliminaries consisting principally of fixed-point theorems and the computational context for the development of validating methods in function spaces. The subsequent chapters deals with the development and application of point of view of ultra-arithmetic and the constructs of function-space arithmetic spaces, such as spaces, bases, rounding, and approximate operations. These topics are followed by discussion of the iterative residual correction methods for function problems and the requirements of a programming language needed to make the tools and constructs of the methodology available in actual practice on a computer. The last chapter describes the techniques for adapting the methodologies to a computer, including the self-validating results for specific problems. This book will prove useful to mathematicians and advance mathematics students.
Download or read book Scientific Computing Validated Numerics Interval Methods written by Walter Krämer and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scan 2000, the GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics and Interval 2000, the International Conference on Interval Methods in Science and Engineering were jointly held in Karlsruhe, September 19-22, 2000. The joint conference continued the series of 7 previous Scan-symposia under the joint sponsorship of GAMM and IMACS. These conferences have traditionally covered the numerical and algorithmic aspects of scientific computing, with a strong emphasis on validation and verification of computed results as well as on arithmetic, programming, and algorithmic tools for this purpose. The conference further continued the series of 4 former Interval conferences focusing on interval methods and their application in science and engineering. The objectives are to propagate current applications and research as well as to promote a greater understanding and increased awareness of the subject matters. The symposium was held in Karlsruhe the European cradle of interval arithmetic and self-validating numerics and attracted 193 researchers from 33 countries. 12 invited and 153 contributed talks were given. But not only the quantity was overwhelming we were deeply impressed by the emerging maturity of our discipline. There were many talks discussing a wide variety of serious applications stretching all parts of mathematical modelling. New efficient, publicly available or even commercial tools were proposed or presented, and also foundations of the theory of intervals and reliable computations were considerably strengthened.
Download or read book Computer Arithmetic and Validity written by Ulrich Kulisch and published by Walter de Gruyter. This book was released on 2013-04-30 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the revised and extended second edition of the successful basic book on computer arithmetic. It is consistent with the newest recent standard developments in the field. The book shows how the arithmetic and mathematical capability of the digital computer can be enhanced in a quite natural way. The work is motivated by the desire and the need to improve the accuracy of numerical computing and to control the quality of the computed results (validity). The accuracy requirements for the elementary floating-point operations are extended to the customary product spaces of computations including interval spaces. The mathematical properties of these models are extracted into an axiomatic approach which leads to a general theory of computer arithmetic. Detailed methods and circuits for the implementation of this advanced computer arithmetic on digital computers are developed in part two of the book. Part three then illustrates by a number of sample applications how this extended computer arithmetic can be used to compute highly accurate and mathematically verified results. The book can be used as a high-level undergraduate textbook but also as reference work for research in computer arithmetic and applied mathematics.
Download or read book SCAN 89 written by Universität Basel and published by . This book was released on 1989 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Applications of Interval Computations written by R. Baker Kearfott and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: Primary Audience for the Book • Specialists in numerical computations who are interested in algorithms with automatic result verification. • Engineers, scientists, and practitioners who desire results with automatic verification and who would therefore benefit from the experience of suc cessful applications. • Students in applied mathematics and computer science who want to learn these methods. Goal Of the Book This book contains surveys of applications of interval computations, i. e. , appli cations of numerical methods with automatic result verification, that were pre sented at an international workshop on the subject in EI Paso, Texas, February 23-25, 1995. The purpose of this book is to disseminate detailed and surveyed information about existing and potential applications of this new growing field. Brief Description of the Papers At the most fundamental level, interval arithmetic operations work with sets: The result of a single arithmetic operation is the set of all possible results as the operands range over the domain. For example, [0. 9,1. 1] + [2. 9,3. 1] = [3. 8,4. 2], where [3. 8,4. 2] = {x + ylx E [0. 9,1. 1] and y E [3. 8,4. 2]}. The power of interval arithmetic comes from the fact that (i) the elementary operations and standard functions can be computed for intervals with formulas and subroutines; and (ii) directed roundings can be used, so that the images of these operations (e. g.
Download or read book Fundamentals of Numerical Computation Computer Oriented Numerical Analysis written by G. Alefeld and published by Springer. This book was released on 1980-12-31 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains mainly a collection of the invited lectures which were given during a conference on "Fundamentals of Numerical Computation", held in June, 5 - 8, 1979, on the occasion of the centennial of the Technical University of Berlin. About hundred scientists from several countries attended this conference. A preceding meeting on "Fundamentals of Computer-Arithmetic" was held in August, 1975, at the "Mathematisches Forschungsinstitut Oberwolfach". The lectures of this conference have been published as Supplementum 1 of Computing (Editors R. Albrecht, U. Kulisch). After a period of four years of active research the purpose of the Berlin-Conference was to give a broad survey of the present status of the closely connected topics Interval Analysis, Mathematical Foundation of Computer Arithmetic, Rounding Error Analysis and Stability of Numerical Algorithms and to give prospects of future activities in these fields. Besides the invited lectures 35 short com munications, each of 20 minutes length, were given. We gratefully acknowledge the support of the President of the Technical University and of his Aussenreferat as well as of the Department of Mathematics. Besides these institutions financial support was given by AEG-Telefunken, Berlin, Allianz Lebensversicherungs A.G., Stuttgart, CDC, Hamburg/Berlin, DAT A 100, Munchen, Gesellschaft von Freunden der TU Berlin e.V., Berlin and Siemens AG., Berlin. Finally we express our thanks to Mrs. G. Froehlich and Mrs. B. Trajanovic, who managed the paper work before, during and after the conference.
Download or read book Scientific Computing Computer Arithmetic and Validated Numerics written by Marco Nehmeier and published by Springer. This book was released on 2016-04-08 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed post proceedings of the 16th International Symposium, SCAN 2014, held in Würzburg, Germany, in September 2014. The 22 full papers presented were carefully reviewed and selected from 60 submissions. The main concerns of research addressed by SCAN conferences are validation, verification or reliable assertions of numerical computations. Interval arithmetic and other treatments of uncertainty are developed as appropriate tools.
Download or read book Interval Analysis written by Günter Mayer and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-04-10 with total page 625 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained text is a step-by-step introduction and a complete overview of interval computation and result verification, a subject whose importance has steadily increased over the past many years. The author, an expert in the field, gently presents the theory of interval analysis through many examples and exercises, and guides the reader from the basics of the theory to current research topics in the mathematics of computation. Contents Preliminaries Real intervals Interval vectors, interval matrices Expressions, P-contraction, ε-inflation Linear systems of equations Nonlinear systems of equations Eigenvalue problems Automatic differentiation Complex intervals
Download or read book Validation Numerics written by R. Albrecht and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles in this book give a comprehensive overview on the whole field of validated numerics. The problems covered include simultaneous systems of linear and nonlinear equations, differential and integral equations and certain applications from technical sciences. Furthermore some papers which improve the tools are included. The book is a must for scientists working in numerical analysis, computer science and in technical fields.
Download or read book Validated Numerics written by Warwick Tucker and published by Princeton University Press. This book was released on 2011-07-05 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive, self-contained primer on validated numerics This textbook provides a comprehensive introduction to the theory and practice of validated numerics, an emerging new field that combines the strengths of scientific computing and pure mathematics. In numerous fields ranging from pharmaceutics and engineering to weather prediction and robotics, fast and precise computations are essential. Based on the theory of set-valued analysis, a new suite of numerical methods is developed, producing efficient and reliable solvers for numerous problems in nonlinear analysis. Validated numerics yields rigorous computations that can find all possible solutions to a problem while taking into account all possible sources of error—fast, and with guaranteed accuracy. Validated Numerics offers a self-contained primer on the subject, guiding readers from the basics to more advanced concepts and techniques. This book is an essential resource for those entering this fast-developing field, and it is also the ideal textbook for graduate students and advanced undergraduates needing an accessible introduction to the subject. Validated Numerics features many examples, exercises, and computer labs using MATLAB/C++, as well as detailed appendixes and an extensive bibliography for further reading. Provides a comprehensive, self-contained introduction to validated numerics Requires no advanced mathematics or programming skills Features many examples, exercises, and computer labs Includes code snippets that illustrate implementation Suitable as a textbook for graduate students and advanced undergraduates
Download or read book Validation Numerics written by Rudolf F. Albrecht and published by Springer. This book was released on 1993 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Application Specific Processors written by Earl E. Swartzlander Jr. and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Application Specific Processors is written for use by engineers who are developing specialized systems (application specific systems). Traditionally, most high performance signal processors have been realized with application specific processors. The explanation is that application specific processors can be tailored to exactly match the (usually very demanding) application requirements. The result is that no `processing power' is wasted for unnecessary capabilities and maximum performance is achieved. A disadvantage is that such processors have been expensive to design since each is a unique design that is customized to the specific application. In the last decade, computer-aided design systems have been developed to facilitate the development of application specific integrated circuits. The success of such ASIC CAD systems suggests that it should be possible to streamline the process of application specific processor design. Application Specific Processors consists of eight chapters which provide a mixture of techniques and examples that relate to application specific processing. The inclusion of techniques is expected to suggest additional research and to assist those who are faced with the requirement to implement efficient application specific processors. The examples illustrate the application of the concepts and demonstrate the efficiency that can be achieved via application specific processors. The chapters were written by members and former members of the application specific processing group at the University of Texas at Austin. The first five chapters relate to specific arithmetic which often is the key to achieving high performance in application specific processors. The next two chapters focus on signal processing systems, and the final chapter examines the interconnection of possibly disparate elements to create systems.
Download or read book Computerarithmetic written by Edgar W. Kaucher and published by . This book was released on 1987 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.
