Fundamentals of Numerical Computation (Computer-Oriented Numerical Analysis)

Description

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