Choosing Kernel Shape Parameters in Partition of Unity Methods by Univariate Global Optimization Techniques

In this paper, we present a numerical scheme to select the kernel shape parameters within partition of unity methods. In an interpolation framework, we propose the use of a leave-one-out cross validation technique combined with efficient global optimization tools from the class of Lipschitz derivative-free methods. Numerical results highlight how this union is generally able to produce some enhancements in terms of both efficiency and accuracy.