Customer Reviews

Meshfree Approximation Methods with MATLAB (Interdisciplinary Mathematical Sciences)

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I loved this book because of the practical aspect and the Matlab codes it provides. This makes the subject very easy to understand.
I had read many papers on the subject of meshfree approximations but most of them keep repeating the same theoretical aspect. This book shows you how you can actually impliment it.
Seeing the implimentation of meshfree approximation methods, I was able to better understand the theoretical aspect of it.
The only unfortunate thing in this book is that the part dealing with the solution of differential equations is somewhat brief. However, this is just a minor thing as all the essential tools to be able to apply the methods to solve differential equations are provided.

This book is an excellent text. The use of radial basis functions for approximation and collocation is widespread, but there are few texts which provide both the theoretical foundation and application of their use. Greg Fasshauer has produced an extremely useful guide for both novices and experts and it will certainly be around for some time.

The two real tests of a practical guide on a technical subject consist of how well the guide facilitates transfer of concepts to your applications and how quickly does that happen. I am happy to say that Gregory Fasshauer's new book on Meshfree Aproximation Methods with MatLab passes both tests with flying colors (Happy because it means that I didn't just blow 50 bucks for nothing!). I find the exposition to be clear and well-developed. The author builds up concepts in a very organized and logically consistent manner. The examples and code listings make it simple to start making immediate use of the techniques discussed in the book. The range of coverage is also very good, starting from simple scattered data interpolation (with discussion of optimality), to compactly-supported RBF to moving least squares methods, to Hermite interpolation to RBF Galerkin methods and more. The author also provides an extensive bibliography to lead you to more detailed or deeper expositions of the material. This book is a great jumping off point for more theoretical treatments such as found in the books by Buhmann and Wendland or in the research literature. With the paperback edition out at a reasonable price, there is no reason not to get this book.