Reliability in Computing

Contributors

Preface

Acknowledgments


1. Computer Arithmetic and Mathematical Software

Arithmetic for Vector Processors

FORTRAN-SC, A FORTRAN Extension for Engineering/Scientific Computation with Access to ACRITH: Language Description with Examples

FORTRAN-SC A FORTRAN Extension for Engineering/Scientific

Computation with Access to ACRITH: Demonstration of the Compiler and Sample Programs

Reliable Expression Evaluation in PASCAL-SC

Floating-Point Standards—Theory and Practice

Algorithms for Verified Inclusions—Theory and Practice

Applications of Differentiation Arithmetic


2. Linear and Nonlinear Systems

Interval Acceleration of Convergence

Solving Systems of Linear Interval Equations

Interval Least Squares—A Diagnostic Tool

Existence of Solutions and Iterations for Nonlinear Equations

Interval Method for Algebraic Equations

Error Questions in the Computation of Solution Manifolds of Parametrized Equations

The Enclosure of Solutions of Parameter-Dependent Systems of Equations


3. Optimization

An Overview of Global Optimization Using Interval Analysis

Philosophy and Practicalities of Interval Arithmetic

Some Recent Aspects of Interval Algorithms for Global Optimization

The Use of Interval Arithmetic in Uncovering Structure of Linear Systems


4. Operator Equations

The Role of Order in Computing

Interval Methods for Operator Equations

Boundary Implications for Stability Properties: Present Status

Validating Computation in a Function Space

Epilogue: A Poem about My Life, by Daniel J. Langton