ebook ebooks e-book e-books downloaden bei MyEbooks.ch downloaden

Computer Arithmetic and Validity Theory, Implementation, and Applications

:	Ulrich Kulisch
:	Computer Arithmetic and Validity Theory, Implementation, and Applications
:	Walter de Gruyter GmbH& Co.KG
:	9783110301793
:	De Gruyter Studies in MathematicsISSN
:	1
:	CHF 148.50
:

:	Mathematik
:	English

:	456
:	Wasserzeichen
:	PC/MAC/eReader/Tablet
:	PDF

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 capability of the computer can be enhanced. 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 and lead to a general theory of computer arithmetic. Detailed methods and circuits for the implementation of this advanced computer arithmetic are developed in the book. It illustrates how the extended 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.

< >Ulrich Kulisch, University Karlsruhe, Germany.

	Foreword to the second edition	7
	Preface	9
	Introduction	23
	I Theory of computer arithmetic	33
	1 First concepts	35
	1.1 Ordered sets	35
	1.2 Complete lattices and complete subnets	40
	1.3 Screens and roundings	46
	1.4 Arithmetic operations and roundings	57
	2 Ringoids and vectoids	65
	2.1 Ringoids	65
	2.2 Vectoids	76
	3 Definition of computer arithmetic	84
	3.1 Introduction	84
	3.2 Preliminaries	87
	3.3 The traditional definition of computer arithmetic	91
	3.4 Definition of computer arithmetic by semimorphisms	92
	3.5 A remark about roundings	100
	3.6 Uniqueness of the minus operator	101
	3.7 Rounding near zero	103
	4 Interval arithmetic	109
	4.1 Interval sets and arithmetic	110
	4.2 Interval arithmetic over a linearly ordered set	119
	4.3 Interval matrices	123
	4.4 Interval vectors	129
	4.5 Interval arithmetic on a screen	132
	4.6 Interval matrices and interval vectors on a screen	140
	4.7 Complex interval arithmetic	148
	4.8 Complex interval matrices and interval vectors	154
	4.9 Extended interval arithmetic	159
	4.10 Exception-free arithmetic for extended intervals	163
	4.11 Extended interval arithmetic on the computer	168
	4.12 Exception-free arithmetic for closed real intervals on the computer	171
	4.13 Comparison relations and lattice operations	174
	4.14 Algorithmic implementation of interval multiplication and division	175
	II Implementation of arithmetic on computers	177
	5 Floating-point arithmetic	179
	5.1 Definition and properties of the real numbers	179
	5.2 Floating-point numbers and roundings	185
	5.3 Floating-point operations	194
	5.4 Subnormal floating-point numbers	202
	5.5 On the IEEE floating-point arithmetic standard	203
	6 Implementation of floating-point arithmetic on a computer	213
	6.1 A brief review of the realization of integer arithmetic	214
	6.2 Introductory remarks about the level 1 operations	223
	6.3 Addition and subtraction	228
	6.4 Normalization	232
	6.5 Multiplication	234
	6.6 Division	234
	6.7 Rounding	236
	6.8 A universal rounding unit	238
<