β Scribed by Prof. Dr.-Ing. E. Adams (auth.), Prof. Dr. GΓΆtz Alefeld, Prof. Dr. Rolf Dieter Grigorieff (eds.)
No coin nor oath required. For personal study only.
Front Matter....Pages i-vii
On Methods for the Construction of the Boundaries of Sets of Solutions for Differential Equations or Finite-Dimensional Approximations with Input Sets....Pages 1-16
Roundings and Approximations in Ordered Sets....Pages 17-31
Interval Analysis in the Extended Interval Space IR ....Pages 33-49
Arithmetic Operations in Interval Spaces....Pages 51-67
Some Applications of Extended Interval Arithmetic to Interval Iterations....Pages 69-84
Foundations of Finite Precision Rational Arithmetic....Pages 85-111
Interval Methods for Nonlinear Systems....Pages 113-120
Algorithms for Multiplication with Given Precision....Pages 121-129
Unrestricted Algorithms for Generating Elementary Functions....Pages 131-140
Applications of Software for Automatic Differentiation in Numerical Computation....Pages 141-156
Small Bounds for the Solution of Systems of Linear Equations....Pages 157-164
Shorthand Notation for Rounding Errors....Pages 165-168
Rounding Error Analysis of Elementary Numerical Algorithms....Pages 169-195
Iterative Methods in the Spaces of Rounded Computations....Pages 197-209
Portable Software for Interval Arithmetic....Pages 211-229
Numerical Analysis
π SIMILAR VOLUMES
This book examines the solution of some of the most common problems of numerical computation. By concentrating on one effective algorithm for each basic task, it develops the fundamental theory in a brief, elementary way. There are ample exercises, and codes are provided to reduce the time otherwise
Fundamentals of Numerical Computation?is an advanced undergraduate-level introduction to the mathematics and use of algorithms for the fundamental problems of numerical computation: linear algebra, finding roots, approximating data and functions, and solving differential equations. The book is organ
<i>If mathematical modeling is the process of turning real phenomena into mathematical abstractions, then numerical computation is largely about the transformation from abstract mathematics to concrete reality. Many science and engineering disciplines have long benefited from the tremendous value of