Gaston Gonnet and Ralf Scholl have written an interesting book entitled Scientific Computation. The title of the book, however, may be misleading. The book is specifically about optimization, not scientific computing in general.There is nothing in the book, for example, about differential equations or several other topics one might expect from a book with such a gereral title. On the other hand, many scientific problems may be formulated as optimization problems.
The best feature of the book is the emphasis on concrete applications. Applications always precede and motivate algorithms. For instance, the first chapter is entitled “Determination of the accurate location of an aircraft.” The algorithmic content of the chapter is least squares optimization, motivated by the problem of locating aircraft. The book goes into interesting details such as the difference between two kinds of beacons, very high frequency ominirange (VOR) and distance measuring equipment (DME).
Most of the applications in Scientific Computing come from biology. Half of the book’s eight chapters are devoted to the problem of determining the secondary structure of proteins and one chapter is devoted to constructing phylogenetic trees. However, the book also contains a variety of applications outside of biology. One chapter is devoted to stock market prediction. A number of other applications are presented, though in less depth. In the context of these applications, the book introduces a variety of algorithms and techniques: modelling using least squares, singular value decomposition, linear programming, dynamic programming, etc.
Scientific Computing gives brief but helpful introductions to its various areas of application.Applications are followed by insightful comments on interpretation and practical aspects of the solution.
There is not a lot of mathematics in the book; the emphasis is on application rather than theory. The book often cites popular works (e.g. Numerical Recipes and Wikipedia) rather than more in-depth resources. Scientific Computing could be a suitable textbook for a computer science course surveying problems in scientific computing; that is the context in which the book was developed. A more mathematical course in optimization might use Scientific Computing not as a primary text but as a valuable source of additional applications, particularly for students interested in biology.
John D. Cook is a research statistician at M. D. Anderson Cancer Center and a blogger.