![]() ![]() ![]() Algorithms are presented primarily via MATLAB code, along with detailed explanations of the code. He carefully threads the presentation to include the mathematics, convergence theory, algorithm design, and results for one-dimensional and higher-dimensional problems. He specifically focuses on the principle aspects of meshfree methods that involve moving least squares (MLS) and radial basis functions (RBFs). In fact, Fasshauer provides linkages of meshfree techniques to these other approaches for solving PDEs. In a thorough preface, the author reviews the development of approximation methods, from finite-difference methods, to finite-element and spectral methods, and finally, beginning in the 1980s, to meshfree methods. Additionally, the topic’s application and its use with related software tools-specifically MATLAB-for learning and development make this a valuable reference for many scientists. Fasshauer’s book provides an excellent state-of-the-art review. The topic has advanced greatly, particularly since the golden age of spline function development in the mid-20th century. But, in fact, it is one of the major kernels-as far as linear algebra and special function techniques are concerned-that many highly sophisticated topics rest upon-for example, the multigrid solution of complex systems of nonlinear partial differential equations (PDEs). At first sight, data fitting appears simple and trivial, being one of the basic topics covered in even the most elementary numerical methods courses. ![]() The subject of data fitting, specifically interpolation and approximation, is fundamental in computational science. Meshfree approximation methods with MATLABįasshauer G., World Scientific Publishing Co, Inc., River Edge, NJ, 2007. 520 pp. Type: Book (9789812706348) Computing Reviews, the leading online review service for computing literature. ![]()
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