Overview

The book deals with computer arithmetic in a more general sense than usual. Advanced computer arithmetic requires that all computer approximations of arithmetic operations - in particular those in the usual vector and matrix spaces - differ from the correct result by at most one rounding. The implementation of advanced computer arithmetic by fast hardware is examined in the book. The new expanded computational capability is gained at modest cost. It increases both the speed of a computation and the accuracy of the computed result. With it fast multiple precision arithmetic can be easily provided. All this strongly supports the case for implementing advanced computer arithmetic on every CPU. The book also shows that on superscalar processors interval operations can be made as fast as simple floating-point operations with only very modest additional hardware costs.

Full Product Details

Author:   Ulrich W. Kulisch
Publisher:   Springer Verlag GmbH
Imprint:   Springer Verlag GmbH
Edition:   Softcover reprint of the original 1st ed. 2002
Dimensions:   Width: 15.50cm , Height: 1.30cm , Length: 23.50cm
Weight:   0.281kg
ISBN:  

9783211838709

ISBN 10:   3211838708
Pages:   144
Publication Date:   23 October 2002
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of stock  
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Table of Contents

1. Fast and Accurate Vector Operations.- 1.1 Introduction.- 1.2 Implementation Principles.- 1.3 High-Performance Scalar Product Units (SPU).- 1.4 Comments on the Scalar Product Units.- 1.5.1 Scalar Product Units for Top-Performance Computers.- 1.6 Hardware Accumulation Window.- 1.7 Theoretical Foundation of Advanced Computer Arithmetic.- Bibliography and Related Literature.- 2. Rounding Near Zero.- 2.1 The one dimensional case.- 2.2 Rounding in product spaces.- Bibliography and Related Literature.- 3. Interval Arithmetic Revisited.- 3.1 Introduction and Historical Remarks.- 3.2 Interval Arithmetic, a Powerful Calculus to Deal with Inequalities.- 3.3 Interval Arithmetic as Executable Set Operations.- 3.4 Enclosing the Range of Function Values.- 3.5 The Interval Newton Method.- 3.6 Extended Interval Arithmetic.- 3.7 The Extended Interval Newton Method.- 3.8 Differentiation Arithmetic, Enclosures of Derivatives.- 3.9 Interval Arithmetic on the Computer.- 3.10 Hardware Support for Interval Arithmetic.

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