In an attempt to introduce application scientists and graduate students to the exciting topic of positive definite kernels and radial basis functions, this book presents modern theoretical results on kernel-based approximation methods and demonstrates their implementation in a variety of fields of application. With the aim of providing researchers involved in function approximation, boundary value problems, spatial statistics and machine learning with the flexible and high-order tools developed using kernels, the authors explore their historical context and explain recent advances as strategies to address long-standing problems.The examples are drawn from fields as diverse as surrogate modeling, machine learning and finance, and researchers from those and other fields will be able to follow the examples on their own machines using the included MATLAB code accessible through the library online.In combining the theoretical foundation of positive definite kernels with accessible experimentation from which to build on, the authors are empowering readers to use these powerful tools on their problems of interest.Key Features:○ The examples in this book are drawn from many different fields which will provide all readers with results close to their own interests○ Newer ideas such as generalized Sobolev spaces and alternate/stable bases are developed in a historical context, explaining both these significant new results but also their genesis over many decades○ By using the software library which accompanies the book, application scientists and graduate students can easily study how the authors implemented new theoretical concepts and quickly adapt them to their problems

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