Numerical software is used to test scientific theories, design airplanes and bridges, operate manufacturing lines, control power plants and refineries, analyze financial derivatives, identify genomes, and provide the understanding necessary to derive and analyze cancer treatments. Because of the high stakes involved, it is essential that results computed using software be accurate, reliable, and robust. Unfortunately, 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 tools to assess existing scientific applications are described, and a variety of techniques that can improve the accuracy and reliability of newly developed applications is discussed. Accuracy and Reliability in Scientific Computing can be considered a handbook for improving the quality of scientific computing. It will help computer scientists address 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. Well-known cases of failure are reviewed and the what and why of numerical computations are considered. 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. The authors of the individual chapters are international experts, many of them members of the IFIP Working Group on Numerical Software. Accuracy and Reliability in Scientific Computing contains condensed information on the main features of six major programming languages — Ada, C, C++, Fortran, Java, and Python — and the INTLAB toolbox of the MATLABâ software and the PRECISE toolbox of Fortran are discussed in detail. This book has an accompanying website, www.nsc.liu.se/wg25/book/, with codes, links, color versions of some illustrations, and additional material. The book will be of interest to any scientist, engineer, or physicist who wants to improve the reliability and accuracy of computed results, especially when the computations are critical or large. It will be of interest to practitioners who use numerical software for real applications and want to avoid potential difficulties. Much of the software available today is poorly written, inadequate in its facilities, and altogether a number of years behind the most advanced state of the art. —Professor Maurice V.Wilkes, September 1973. Scientific software is central to our computerized society. It is used to design airplanes and bridges, to operate manufacturing lines, to control power plants and refineries, to analyze financial derivatives, to map genomes, and to provide the understanding necessary for the diagnosis and treatment of cancer. Because of the high stakes involved, it is essential that the software be accurate and reliable. Unfortunately, developing accurate and reliable scientific software is notoriously difficult, and Maurice Wilkes' assessment of 1973 still rings true today. Not only is scientific software beset with all the well-known problems affecting software development in general, it must cope with the special challenges of numerical computation. Approximations occur at all levels. Continuous functions are replaced by discretized versions. Infinite processes are replaced by finite ones. Real numbers are replaced by finite precision numbers. As a result, errors are built into the mathematical fabric of scientific software which cannot be avoided. At best they can be judiciously managed. The nature of these errors, and how they are propagated, must be understood if the resulting software is to be accurate and reliable. The objective of this book is to investigate the nature of some of these difficulties, and to provide some insight into how to overcome them
This book is about guaranteed numerical methods based on interval analysis for approximating sets, and about the application of these methods to vast classes of engineering problems. Guaranteed means here that inner and outer approximations of the sets of interest are obtained, which can be made as precise as desired, at the cost of increasing the computational effort. It thus becomes possible to achieve tasks still thought by many to be out of the reach of numerical methods, such as finding all solutions of sets of non-linear equations and inequality or all global optimizers of possibly multi-modal criteria.
The basic methodology is explained as simply as possible, in a concrete and readily applicable way, with a large number of figures and illustrative examples. Some of the techniques reported appear in book format for the first time. The ability of the approach advocated here to solve non-trivial engineering problems is demonstrated through examples drawn from the fields of parameter and state estimation, robust control and robotics. Enough detail is provided to allow readers with other applications in mind to grasp their significance.
An in-depth treatment of implementation issues facilitates the understanding and use of freely available software that makes interval computation about as easy as computation with floating-point numbers. The reader is even given the basic information needed to build his or her own C++ interval library.
At the core of many engineering problems is the solution of sets of equa tions and inequalities, and the optimization of cost functions. Unfortunately, except in special cases, such as when a set of equations is linear in its un knowns or when a convex cost function has to be minimized under convex constraints, the results obtained by conventional numerical methods are only local and cannot be guaranteed. This means, for example, that the actual global minimum of a cost function may not be reached, or that some global minimizers of this cost function may escape detection. By contrast, interval analysis makes it possible to obtain guaranteed approximations of the set of all the actual solutions of the problem being considered. This, together with the lack of books presenting interval techniques in such a way that they could become part of any engineering numerical tool kit, motivated the writing of this book. The adventure started in 1991 with the preparation by Luc Jaulin of his PhD thesis, under Eric Walter's supervision. It continued with their joint supervision of Olivier Didrit's and Michel Kieffer's PhD theses. More than two years ago, when we presented our book project to Springer, we naively thought that redaction would be a simple matter, given what had already been achieved . . . Annotation 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 CD-ROM contains: trial version of Sun Microsystems' Forte Developer 6 for use with Solaris SPARC Platform Edition 2.6, 2.7 and 2.8
