Meshfree approximation methods are a relatively new area of research, and there are only a few books covering it at present. Whereas other works focus almost entirely on theoretical aspects or applications in the engineering field, this book provides the salient theoretical results needed for a basic understanding of meshfree approximation methods. The emphasis here is on a hands-on approach that includes MATLAB routines for all basic operations. Meshfree approximation methods, such as radial basis function and moving least squares method, are discussed from a scattered data approximation and partial differential equations point of view. A good balance is supplied between the necessary theory and implementation in terms of many MATLAB programs, with examples and applications to illustrate key points. Used as class notes for graduate courses at Northwestern University, Illinois Institute of Technology, and Vanderbilt University, this book will appeal to both mathematics and engineering graduate students.
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The author can only be congratulated for this work which will provide useful material for readers for years to come. -- Zentralblatt MATH
The book gives a very readable account of the subject matters with algorithms and Matlab implementations of the algorithms ... This is a good book for an introduction to the subject or for a basic, computationally oriented, course. -- Mathematical Reviews
The author can only be congratulated for this work which will provide useful material for readers for years to come. --Zentralblatt MATH --This text refers to the Hardcover edition.
The book gives a very readable account of the subject matters with algorithms and Matlab implementations of the algorithms ... This is a good book for an introduction to the subject or for a basic, computationally oriented, course. -- Mathematical Reviews
The author can only be congratulated for this work which will provide useful material for readers for years to come. --Zentralblatt MATH --This text refers to the Hardcover edition.
Review
The book gives a very readable account of the subject matters with algorithms and Matlab implementations of the algorithms ... This is a good book for an introduction to the subject or for a basic, computationally oriented, course.
--This text refers to the
Hardcover
edition.
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Most Helpful Customer Reviews
3 of 3 people found the following review helpful:
5.0 out of 5 stars
Excellent,
By Sam (US) - See all my reviews
This review is from: Meshfree Approximation Methods with MATLAB (Interdisciplinary Mathematical Sciences) (Paperback)
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.
2 of 2 people found the following review helpful:
5.0 out of 5 stars
Solid Book,
By Iron Mike (Chicago, IL USA) - See all my reviews
This review is from: Meshfree Approximation Methods With Matlab (Interdisciplinary Mathematical Sciences) (Hardcover)
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.
2 of 2 people found the following review helpful:
5.0 out of 5 stars
Excellent Practical Guide,
By An A.I. Guy (Boston, MA USA) - See all my reviews
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This review is from: Meshfree Approximation Methods with MATLAB (Interdisciplinary Mathematical Sciences) (Paperback)
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.
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Key Phrases - Statistically Improbable Phrases (SIPs):
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stationary interpolation, strictly positive definite functions, definite radial functions, native space norm, boundary collocation points, radial basis function interpolant, scattered data interpolation problem, distinct data sites, generalized multiquadrics, supported radial functions, one point algorithm, multilevel interpolation, multiquadric interpolation, basis function interpolants, cardinal polynomials, conditionally positive definite functions, knot removal algorithm, positive definite radial function, radial basis function interpolation, polyharmonic splines, multiquadric method, collocation matrix, strictly positive definite kernel, moving least squares method, knot insertion algorithm Key Phrases - Capitalized Phrases (CAPs): (learn more)
Define Franke, Central File Exchange, Guy Shechter, Daniel Dougherty, Iterations Fig, Miscellaneous Theory, Optimality Theorem New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
stationary interpolation, strictly positive definite functions, definite radial functions, native space norm, boundary collocation points, radial basis function interpolant, scattered data interpolation problem, distinct data sites, generalized multiquadrics, supported radial functions, one point algorithm, multilevel interpolation, multiquadric interpolation, basis function interpolants, cardinal polynomials, conditionally positive definite functions, knot removal algorithm, positive definite radial function, radial basis function interpolation, polyharmonic splines, multiquadric method, collocation matrix, strictly positive definite kernel, moving least squares method, knot insertion algorithm Key Phrases - Capitalized Phrases (CAPs): (learn more)
Define Franke, Central File Exchange, Guy Shechter, Daniel Dougherty, Iterations Fig, Miscellaneous Theory, Optimality Theorem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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