Introduction to Interval Computation

1st Edition

Authors: Gotz Alefeld Jurgen Herzberger
Hardcover ISBN: 9780120498208
eBook ISBN: 9780080916361
Imprint: Academic Press
Published Date: 28th November 1983
Page Count: 352
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Description

This book is revised and expanded version of the original German text. The arrangement of the material and the structure are essentially unchanged. All remarks in the Preface to the German Edition regarding naming conventions for formulas, theorems, lemmas, and definitions are still valid as are those concerning the arrangement and choice of material.

Readership

Students and Mathematicians.

Table of Contents

Preface to the English Edition. Preface to the German Edition. Real Interval Arithmetic. Further Concepts and Properties. Interval Evaluation and Range of Real Functions. Machine Interval Arithmetic. Complex Interval Arithmetic. Metric, Absolute, Value, and Width in. Inclusion of Zeros of a Function of One Real Variable. Methods for the Simultaneous Inclusion of Real Zeros of Polynomials. Methods for the Simultaneous Inclusion of Complex Zeros of Polynomials. Interval Matrix Operations. Fixed Point Iteration for Nonlinear Systems of Equations. Systems of Linear Equations Amenable to Interation. Optimality of the Symmetric Single Step Method with Taking Intersection after Every Component. On the Feasibility of the Gaussian Algorithm for Systems of Equations with Intervals as Coefficients. Hansen's Method. The Procedure of Kupermann and Hansen. Ireation Methods for the Inclusion of the Inverse Matrix and for Triangular Decompositions. Newton-like Methods for Nonlinear Systems of Equations. Newton-like Methods without Matrix Inversions. Newton-like Methods for Particular Systems of Nonlinear Equations. Newton-like Total step and Single Step Methods. Appendix A. The Order of Convergence of Iteration Methods in vn(Ic) and Mmn(iC) ). Appendix B. Realizations of Machine Interval Arithmetics in ALGOL 60. Appendix C. ALGOL Procedures. Bibliography. Index of Notation. Subject Index.

Details

No. of pages:
352
Language:
English
Copyright:
© Academic Press 1983
Published:
Imprint:
Academic Press
eBook ISBN:
9780080916361
Hardcover ISBN:
9780120498208

About the Author

Gotz Alefeld

Affiliations and Expertise

Fakultat Fur Mathematik, Universitat Karlsruhe, Germany

Jurgen Herzberger

Affiliations and Expertise

Fakultat Fur Mathematik, Universitat Oldenburg, Germany

Reviews

This book is revised and expanded version of the original German text. The arrangement of the material and the structure are essentially unchanged. All remarks in the Preface to the German Edition regarding naming conventions for formulas, theorems, lemmas, and definitions are still valid as are those concerning the arrangement and choice of material.