Ebook: Fundamentals of Numerical Computation (Computer-Oriented Numerical Analysis)

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Content:
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

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Content:
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
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