Kernel-based Approximation Methods Using MATLAB

    Kernel-based approximation methods are a class of techniques that use positive definite functions, also known as kernels, to construct high-order and flexible approximations of functions, solutions of differential equations, and statistical models. These methods have been widely used in various fields, such as function approximation, spatial statistics, boundary value problems, machine learning, surrogate modeling, and finance. In this article, we will introduce some basic concepts and properties of kernel-based approximation methods, and show how to implement them using MATLAB.

    What are kernels and kernel-based approximation methods?

    A kernel is a function k that takes two arguments x and y from some domain X, and returns a real number k(x,y) that measures the similarity or correlation between x and y. A kernel is said to be positive definite if for any finite set of points x_1,...,x_n in X and any real numbers c_1,...,c_n, the following inequality holds:




Kernel-based Approximation Methods Using Matlab Pdf 53