The first question that comes to mind is, Why another book on Numerical Analysis? The authors face this question head on and answer it in the preface. They feel that there are books that are strong on theory and books that are strong on algorithmic recipes but that these books do not really capture the current state of scientific computing, which they rightly describe as a “junction of mathematics, computer science, and engineering.” The authors thus set themselves a difficult task, especially since the book is designed for a first course for undergraduate students and also as reference for non-experts that need to apply numerical methods. The result is a hefty volume having over 500 pages, which clearly cannot be fully covered in a one-semester first course.
Fortunately, the authors are experienced practicioners of the art and this shows in the text. While the tone of the prose is often refreshingly informal, the text is both rigorous and sprinkled with nice comments about the practice of scientific computing. The exercises are frequently interesting and so are many examples, such as the PageRank algorithm used by Google, principal component analysis for surface reconstruction from point clouds, image compression with SVD, mesh generation, scattered data interpolation with radial basis functions, image deblurring. These examples are often drawn from the authors’ own research.
In all, an interesting book on numerical methods that has some personality, which is much more that you can say about many other books on the subject.
Luiz Henrique de Figueiredo is a researcher at IMPA in Rio de Janeiro, Brazil. His main interests are numerical methods in computer graphics, but he remains an algebraist at heart. He is also one of the designers of the Lua language.