This book investigates some of the difficulties related to scientific computing, describing how these can be overcome.

Developing accurate and reliable scientific software is notoriously difficult. This book investigates some of the difficulties related to scientific computing and provides insight into how to overcome them and obtain dependable results. The text deals thoroughly with the problems that affect software in general as well as the particular challenges of numerical computation: approximations occurring at all levels, continuous functions replaced by discretized versions, infinite processes replaced by finite ones, and real numbers replaced by finite precision numbers. Divided into three parts, it starts by illustrating some of the difficulties in producing robust and reliable scientific software. The second section describes diagnostic tools that can be used to assess the accuracy and reliability of existing scientific applications. In the last section, the authors describe a variety of techniques that can be employed to improve the accuracy and reliability of newly developed scientific applications.

Preface
Part I. Pitfalls in Numerical Computation:
1. What can go wrong in scientific computing? Bo Einarsson
2. Assessment of accuracy and reliability Ronald F. Boisvert, Ronald Cools and Bo Einarsson
3. Approximating integrals, estimating errors and giving the wrong solution for a deceptively easy problem Ronald Cools
4. An introduction to the quality of computed solutions Sven Hammarling
5. Qualitative computing Fran se Chaitin-Chatelin and Elisabeth Traviesas-Cassan
Part II. Diagnostic Tools: 6. PRECISE and the quality of reliable numerical software Fran se Chaitin-Chatelin and Elisabeth Traviesas-Cassan
7. Tools for the verification of approximate solutions to differential equations Wayne H. Enright
Part III. Technology for Improving Accuracy and Reliability: 8. General methods for implementing reliable and correct software Bo Einarsson
9. The use and implementation of interval data types G. William Walster
10. Computer-assisted proofs and self-validating methods Siegfried M. Rump
11. Hardware assisted algorithms Craig C. Douglas and Hans Petter Langtangen
12. Issues in accurate and reliable use of parallel computing in numerical programs William D. Gropp
13. Software reliability engineering of numerical systems Mladen A. Vouk
Bibliography
Index.