Approximations every where you turn, continuous functions replaced by
discretized versions, infinite processes turned into finite ones, real
numbers replaced by finite precision: errors are built into the
mathematical fabric of scientific software and cannot be avoided, only
managed. Computer scientists in academic, government, and corporate
laboratories around the world explicate the nature of some of the
difficulties and provide some insight into how to overcome them. They cover
pitfalls in numerical computation, diagnostic tools, and technology for
improving accuracy and reliability.
Table Of Contents:
List of Contributors
List of Figures
List of Tables
Part I: PITFALLS IN NUMERICAL COMPUTATION.
Chapter 1: What Can Go Wrong in Scientific Computing?
Chapter 2: Assessment of Accuracy and Reliability
Chapter 3: Approximating Integrals, Estimating Errors, and Giving the Wrong
Solution for a Deceptively Easy Problem
Chapter 4: An Introduction to the Quality of Computed Solutions
Chapter 5: Qualitative Computing
Part II: DIAGNOSTIC TOOLS.
Chapter 6: PRECISE and the Quality of Reliable Numerical Software
Chapter 7: Tools for the Verification of Approximate Solutions to Differential
Part III: TECHNOLOGY FOR IMPROVING ACCURACY AND RELIABILITY.
Chapter 8: General Methods forImplementing Reliable and Correct Software
Chapter 9: The Use and Implementation of Interval Data Types
Chapter 10: Computer-Assisted Proofs and Self-Validating Methods
Chapter 11: Hardware Assisted Algorithms
Chapter 12: Issues in Accurate and Reliable Use of Parallel Computing in Numerical Programs
Chapter 13: Software Reliability Engineering of Numerical Systems