Finite Precision Number Systems And Arithmetic
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Finite Precision Number Systems And Arithmetic
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Author : Peter Kornerup
language : en
Publisher: Cambridge University Press
Release Date : 2010-09-30
Finite Precision Number Systems And Arithmetic written by Peter Kornerup and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-30 with Mathematics categories.
Fundamental arithmetic operations support virtually all of the engineering, scientific, and financial computations required for practical applications, from cryptography, to financial planning, to rocket science. This comprehensive reference provides researchers with the thorough understanding of number representations that is a necessary foundation for designing efficient arithmetic algorithms. Using the elementary foundations of radix number systems as a basis for arithmetic, the authors develop and compare alternative algorithms for the fundamental operations of addition, multiplication, division, and square root with precisely defined roundings. Various finite precision number systems are investigated, with the focus on comparative analysis of practically efficient algorithms for closed arithmetic operations over these systems. Each chapter begins with an introduction to its contents and ends with bibliographic notes and an extensive bibliography. The book may also be used for graduate teaching: problems and exercises are scattered throughout the text and a solutions manual is available for instructors.
Lectures On Finite Precision Computations
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Author : Francoise Chaitin-Chatelin
language : en
Publisher: SIAM
Release Date : 1996-01-01
Lectures On Finite Precision Computations written by Francoise Chaitin-Chatelin and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-01-01 with Mathematics categories.
Mathematics of Computing -- Numerical Analysis.
Fundamentals Of Numerical Computation Computer Oriented Numerical Analysis
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Author : G. Alefeld
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Fundamentals Of Numerical Computation Computer Oriented Numerical Analysis written by G. Alefeld and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Finite Precision Number Systems And Arithmetic
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Author : Peter Kornerup
language : en
Publisher: Cambridge University Press
Release Date : 2010-09-30
Finite Precision Number Systems And Arithmetic written by Peter Kornerup and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-30 with Mathematics categories.
This comprehensive reference volume, suitable for graduate teaching, includes problems, exercises, solutions and an extensive bibliography.
Computer Number Systems And Arithmetic
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Author : Norman Ross Scott
language : en
Publisher: Prentice Hall
Release Date : 1985
Computer Number Systems And Arithmetic written by Norman Ross Scott and has been published by Prentice Hall this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Mathematics categories.
Accuracy And Stability Of Numerical Algorithms
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Author : Nicholas J. Higham
language : en
Publisher: SIAM
Release Date : 2002-01-01
Accuracy And Stability Of Numerical Algorithms written by Nicholas J. Higham and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-01 with Mathematics categories.
Accuracy and Stability of Numerical Algorithms gives a thorough, up-to-date treatment of the behavior of numerical algorithms in finite precision arithmetic. It combines algorithmic derivations, perturbation theory, and rounding error analysis, all enlivened by historical perspective and informative quotations. This second edition expands and updates the coverage of the first edition (1996) and includes numerous improvements to the original material. Two new chapters treat symmetric indefinite systems and skew-symmetric systems, and nonlinear systems and Newton's method. Twelve new sections include coverage of additional error bounds for Gaussian elimination, rank revealing LU factorizations, weighted and constrained least squares problems, and the fused multiply-add operation found on some modern computer architectures.
Computer Arithmetic
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Author : Earl E Swartzlander
language : en
Publisher: World Scientific
Release Date : 2015-03-17
Computer Arithmetic written by Earl E Swartzlander and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-17 with Mathematics categories.
This is the new edition of the classic book Computer Arithmetic in three volumes published originally in 1990 by IEEE Computer Society Press. As in the original, the book contains many classic papers treating advanced concepts in computer arithmetic, which is very suitable as stand-alone textbooks or complementary materials to textbooks on computer arithmetic for graduate students and research professionals interested in the field. Told in the words of the initial developers, this book conveys the excitement of the creators, and the implementations provide insight into the details necessary to realize real chips. This second volume presents topics on error tolerant arithmetic, digit on-line arithmetic, number systems, and now in this new edition, a topic on implementations of arithmetic operations, all wrapped with an updated overview and a new introduction for each chapter. This volume is part of a 3 volume set: Computer Arithmetic Volume I Computer Arithmetic Volume II Computer Arithmetic Volume III The full set is available for sale in a print-only version. Contents:Error Tolerant ArithmeticOn-Line ArithmeticVLSI Adder ImplementationsVLSI Multiplier ImplementationsFloating-Point VLSI ChipsNumber RepresentationImplementations Readership: Graduate students and research professionals interested in computer arithmetic. Key Features:It reprints the classic papersIt covers advanced arithmetic operationsIt does this in the words of the original creatorsKeywords:Computer Arithmetic;Fault Tolerant;Arithmetic;On-Line Arithmetic;Adder Implementations;Multiplier Implementations;Floating Point Chips;Number Representation;Implementations
Krylov Methods For Nonsymmetric Linear Systems
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Author : Gérard Meurant
language : en
Publisher: Springer Nature
Release Date : 2020-10-02
Krylov Methods For Nonsymmetric Linear Systems written by Gérard Meurant and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-02 with Mathematics categories.
This book aims to give an encyclopedic overview of the state-of-the-art of Krylov subspace iterative methods for solving nonsymmetric systems of algebraic linear equations and to study their mathematical properties. Solving systems of algebraic linear equations is among the most frequent problems in scientific computing; it is used in many disciplines such as physics, engineering, chemistry, biology, and several others. Krylov methods have progressively emerged as the iterative methods with the highest efficiency while being very robust for solving large linear systems; they may be expected to remain so, independent of progress in modern computer-related fields such as parallel and high performance computing. The mathematical properties of the methods are described and analyzed along with their behavior in finite precision arithmetic. A number of numerical examples demonstrate the properties and the behavior of the described methods. Also considered are the methods’ implementations and coding as Matlab®-like functions. Methods which became popular recently are considered in the general framework of Q-OR (quasi-orthogonal )/Q-MR (quasi-minimum) residual methods. This book can be useful for both practitioners and for readers who are more interested in theory. Together with a review of the state-of-the-art, it presents a number of recent theoretical results of the authors, some of them unpublished, as well as a few original algorithms. Some of the derived formulas might be useful for the design of possible new methods or for future analysis. For the more applied user, the book gives an up-to-date overview of the majority of the available Krylov methods for nonsymmetric linear systems, including well-known convergence properties and, as we said above, template codes that can serve as the base for more individualized and elaborate implementations.
Number Systems And The Foundations Of Analysis
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Author : Elliott Mendelson
language : en
Publisher:
Release Date : 1985
Number Systems And The Foundations Of Analysis written by Elliott Mendelson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Mathematics categories.
The Number Systems Of Analysis
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Author : C H C Little
language : en
Publisher: World Scientific Publishing Company
Release Date : 2003-09-05
The Number Systems Of Analysis written by C H C Little and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-09-05 with Mathematics categories.
Although students of analysis are familiar with real and complex numbers, few treatments of analysis deal with the development of such numbers in any depth. An understanding of number systems at a fundamental level is necessary for a deeper grasp of analysis. Beginning with elementary concepts from logic and set theory, this book develops in turn the natural numbers, the integers and the rational, real and complex numbers. The development is motivated by the need to solve polynomial equations, and the book concludes by proving that such equations have solutions in the complex number system.