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Computer Arithmetic and Self-Validating Numerical Methods

Author: Christian Ullrich

Publisher: Academic Press

Published: 2014-05-10

Total Pages: 316

ISBN-13: 1483267814

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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.

Book Synopsis Computer Arithmetic and Self-Validating Numerical Methods by : Christian Ullrich

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.

Contributions to Computer Arithmetic and Self-validating Numerical Methods

Author: Christian Ullrich

Publisher:

Published: 1990

Total Pages: 526

ISBN-13:

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Mathematics of Computing -- Numerical Analysis.

Book Synopsis Contributions to Computer Arithmetic and Self-validating Numerical Methods by : Christian Ullrich

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.

Contribution to Computer Arithmetic and Self-validating Numerical Methods

Author: Christian Ullrich

Publisher:

Published: 1990

Total Pages: 526

ISBN-13:

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Book Synopsis Contribution to Computer Arithmetic and Self-validating Numerical Methods by : Christian Ullrich

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:

Contributions to Computer Arithmetic and Self-validating Numerical Methods

Author: Christian Ullrich

Publisher:

Published: 1993

Total Pages: 526

ISBN-13:

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Book Synopsis Contributions to Computer Arithmetic and Self-validating Numerical Methods by : Christian Ullrich

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:

SCAN 89

Author: Universität Basel

Publisher:

Published: 1989

Total Pages:

ISBN-13:

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Book Synopsis SCAN 89 by : Universität Basel

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:

Self-Validating Numerics for Function Space Problems

Author: Edgar W. Kaucher

Publisher: Elsevier

Published: 2014-06-20

Total Pages: 270

ISBN-13: 1483273776

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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.

Book Synopsis Self-Validating Numerics for Function Space Problems by : Edgar W. Kaucher

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.

Computer Arithmetic and Validity

Author: Ulrich Kulisch

Publisher: Walter de Gruyter

Published: 2013-04-30

Total Pages: 456

ISBN-13: 3110301792

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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.

Book Synopsis Computer Arithmetic and Validity by : Ulrich Kulisch

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.

Applications of Interval Computations

Author: R. Baker Kearfott

Publisher: Springer Science & Business Media

Published: 2013-12-01

Total Pages: 435

ISBN-13: 1461334403

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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.

Book Synopsis Applications of Interval Computations by : R. Baker Kearfott

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.

Scientific Computing, Computer Arithmetic, and Validated Numerics

Author: Marco Nehmeier

Publisher: Springer

Published: 2016-04-08

Total Pages: 291

ISBN-13: 3319317695

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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.

Book Synopsis Scientific Computing, Computer Arithmetic, and Validated Numerics by : Marco Nehmeier

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.

Application Specific Processors

Author: Earl E. Swartzlander Jr.

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 266

ISBN-13: 1461314577

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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.

Book Synopsis Application Specific Processors by : Earl E. Swartzlander Jr.

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.