Front Cover; Reliability in Computing: The Role of Interval Methods in Scientific Computing; Copyright Page; Table of Contents; Contributors; Preface; Acknowledgments; Part 1: Computer Arithmetic and Mathematical Software; Chapter 1. ARITHMETIC FOR VECTOR PROCESSORS; ABSTRACT; 1. INTRODUCTION; 2. THE STATE OF THE ART; 3. FAST COMPUTATION OF SUMS AND SCALAR PRODUCTS; 4. SUMMATION WITH ONLY ONE ROW OF ADDERS; 5. SYSTEMS WITH LARGE EXPONENT RANGE AND FURTHER REMARKS; 6. APPLICATION TO MULTIPLE PRECISION ARITHMETIC; 7. CONTEMPORARY FLOATING-POINT ARITHMETIC; 8. LITERATURE.

Chapter 2. FORTRAN-SC, A FORTRAN Extension for Engineering/Scientific Computation with Access to ACRITH: Language Description with ExamplesAbstract; 1. Introduction; 2. Development of FORTRAN-SC; 3. Main Language Concepts; 4. Language Description with Examples; 5. Implementation of FORTRAN-SC; References; Chapter 3. FORTRAN-SC A FORTRAN Extension for Engineering/Scientific Computation with Access to ACRITH: Demonstration of the Compiler and Sample Programs; Abstract; Introduction; Example 1 : Interval Newton Method; Example 2 : Automatic Differentiation; Example 3 : Runge-Kutta Method.

Example 4 : Gaussian Elimination MethodExample 5 : Verified Solution of a Linear System; References; Chapter 4. Reliable Expression Evaluation in PASCAL-SC; Abstract; 1. Floating-point arithmetic; 2. Interval arithmetic; 3. The optimal scalar product; 4. Complex floating-point and complex interval arithmetic; 5. Matrix and vector arithmetic; 6. Accurate Operations and Problem Solving Routines; 7. Transformation of arithmetic expressions; 8. Solution of nonlinear systems; 9. The data type dotprecision; 10. Dotproduct expressions; 11. Conclusion; References.

Chapter 5. Floating-Point Standards -- Theory and Practice1. Introduction; 2. The Standards; 3. Implementations; 4. Software Support; 5. Conclusions; References; Chapter 6. Algorithms for Verified Inclusions: Theory and Practice; Summary; 0. Introduction; 1. Basic theorems; 2. Practical verification on the computer; 3. Interactive Programming Environment; 4. References; Chapter 7. Applications of Differentiation Arithmetic; Abstract; 1. Differentiation Arithmetic -- Why, What, and How?; 2. Why? -- Motivation; 3 . What? -- Component tools; 4. Conditions on f; 5. How to use it? -- Applications.

6. AcknowledgementsReferences; Part 2: Linear and Nonlinear Systems; Chapter 8. INTERVAL ACCELERATION OF CONVERGENCE; Abstract; 1. INTRODUCTION; 2. EXAMPLES; 3. DEFINITIONS AND NOTATION; 4. INTERVAL METHODS; 5. HOW CAN WE GET BOUNDS ON A GIVEN POINT-SEQUENCE?; 6. ACCELERATION OF CONVERGENCE; REFERENCES; Chapter 9. SOLVING SYSTEMS OF LINEAR INTERVAL EQUATIONS; 0. Introduction; 1. Bounding the solutions; 2. Computing the xy's; 3. Explicit formulae for x, x; 4. Inverse interval matrix; References; Chapter 10. Interval Least Squares -- a Diagnostic Tool; Introduction; Linearity; Interval Notation.