Fundamentals of Numerical Computation (Computer-Oriented Numerical Analysis)

Inhaltsverzeichnis

• On Methods for the Construction of the Boundaries of Sets of Solutions for Differential Equations or Finite-Dimensional Approximations with Input Sets.
• Roundings and Approximations in Ordered Sets.
• Interval Analysis in the Extended Interval Space IR.
• Arithmetic Operations in Interval Spaces.
• Some Applications of Extended Interval Arithmetic to Interval Iterations.
• Foundations of Finite Precision Rational Arithmetic.
• Interval Methods for Nonlinear Systems.
• Algorithms for Multiplication with Given Precision.
• Unrestricted Algorithms for Generating Elementary Functions.
• Applications of Software for Automatic Differentiation in Numerical Computation.
• Small Bounds for the Solution of Systems of Linear Equations.
• Shorthand Notation for Rounding Errors.
• Rounding Error Analysis of Elementary Numerical Algorithms.
• Iterative Methods in the Spaces of Rounded Computations.
• Portable Software for Interval Arithmetic.