KERNEL-BASED APPROXIMATION METHODS USING MATLAB (Interdisciplinary Mathematical Sciences)

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 various settings. The authors explore the historical context of this fascinating topic and explain recent advances as strategies to address long-standing problems. Examples are drawn from fields as diverse as function approximation, spatial statistics, boundary value problems, machine learning, surrogate modeling and finance. Researchers from those and other fields can recreate the results within using the documented MATLAB code, also available through the online library. This combination of a strong theoretical foundation and accessible experimentation empowers readers to use positive definite kernels on their own problems of interest.

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.