Computer Arithmetic and Validity - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Computer Arithmetic and Validity write by Ulrich Kulisch. This book was released on 2013-04-30. Computer Arithmetic and Validity available in PDF, EPUB and Kindle. 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.
Validation Numerics
Validation Numerics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Validation Numerics write by R. Albrecht. This book was released on 2012-12-06. Validation Numerics available in PDF, EPUB and Kindle. 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.
Advanced Arithmetic for the Digital Computer
Advanced Arithmetic for the Digital Computer - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Advanced Arithmetic for the Digital Computer write by Ulrich W. Kulisch. This book was released on 2012-09-07. Advanced Arithmetic for the Digital Computer available in PDF, EPUB and Kindle. The number one requirement for computer arithmetic has always been speed. It is the main force that drives the technology. With increased speed larger problems can be attempted. To gain speed, advanced processors and pro gramming languages offer, for instance, compound arithmetic operations like matmul and dotproduct. But there is another side to the computational coin - the accuracy and reliability of the computed result. Progress on this side is very important, if not essential. Compound arithmetic operations, for instance, should always deliver a correct result. The user should not be obliged to perform an error analysis every time a compound arithmetic operation, implemented by the hardware manufacturer or in the programming language, is employed. This treatise deals with computer arithmetic in a more general sense than usual. Advanced computer arithmetic extends the accuracy of the elementary floating-point operations, for instance, as defined by the IEEE arithmetic standard, to all operations in the usual product spaces of computation: the complex numbers, the real and complex intervals, and the real and complex vectors and matrices and their interval counterparts. The implementation of advanced computer arithmetic by fast hardware is examined in this book. Arithmetic units for its elementary components are described. It is shown that the requirements for speed and for reliability do not conflict with each other. Advanced computer arithmetic is superior to other arithmetic with respect to accuracy, costs, and speed.
Computer Arithmetic in Theory and Practice
Computer Arithmetic in Theory and Practice - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Computer Arithmetic in Theory and Practice write by Ulrich W. Kulisch. This book was released on 2014-05-12. Computer Arithmetic in Theory and Practice available in PDF, EPUB and Kindle. Computer Arithmetic in Theory and Practice deals with computer arithmetic and the various implementations of the entire arithmetic package on diverse processors, including microprocessors. It illustrates the importance of theoretical development in the sound implementation of arithmetic on computers, and argues that such an implementation requires the establishment of various isomorphisms between different definitions of arithmetic operations. Comprised of seven chapters, this volume begins with an introduction to the theory of computer arithmetic by giving an axiomatic characterization of the essential properties of sets and subsets; complete lattices and complete subnets; screens and roundings; and arithmetic operations. The discussion then turns to the concepts of a ringoid and a vectoid as well as those of ordered or weakly ordered ringoids and vectoids; interval arithmetic; and floating-point arithmetic. The operations in interval spaces are defined by means of semimorphisms. The final chapter shows how to embed the five basic data types (integer, real, complex, real interval, and complex interval) together with the arithmetic operations that are defined for all of these types into existing higher programming languages. This book will be helpful to students and practitioners in the fields of computer science and applied mathematics.
Computer Arithmetic
Computer Arithmetic - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Computer Arithmetic write by Earl E. Swartzlander. This book was released on 1990. Computer Arithmetic available in PDF, EPUB and Kindle. Mathematics of Computing -- Numerical Analysis.
