In this paper we present a new fast and accurate method for Radial Basis Function (RBF) approximation, including interpolation as special case, which enables us to effectively find the optimal value of RBF shape parameter. particular, propose statistical technique, called Bayesian optimization, that consists in modelling error function with Gaussian process, by which, through an iterative parameter is selected. The process step self-updated resulting relevant decrease search time respect...

Graph signal processing benefits significantly from the direct and highly adaptable supplementary techniques offered by partition of unity methods (PUMs) on graphs. In our approach, we demonstrate generation a solely based underlying graph structure, employing an algorithm that relies exclusively centrality measures modularity, without requiring input number subdomains. Subsequently, integrate PUMs with local basis function (GBF) approximation method to develop cost-effective global...

In this paper, we employ Bayesian optimization to concurrently explore the optimal values for both shape parameter and radius in partition of unity interpolation using radial basis functions. is a probabilistic, iterative approach that models error function through progressively self-updated Gaussian process. Meanwhile, harnesses meshfree method, allowing us significantly reduce computational expenses, particularly when considering substantial number scattered data points. This reduction...

In this article we present an adaptive residual subsampling scheme designed for kernel based interpolation. For optimal choice of the shape parameter consider some cross validation (CV) criteria, using efficient algorithms $k$-fold CV and leave-one-out (LOOCV) as a special case. framework, selection within method is totally automatic, provides highly reliable accurate results any kind kernel, guarantees existence uniqueness interpolant. Numerical show performance new scheme, also giving...

In this paper, Bayesian optimisation is used to simultaneously search the optimal values of shape parameter and radius in radial basis function partition unity interpolation problem. It a probabilistic iterative approach that models error with step-by-step self-updated Gaussian process, whereas leverages mesh-free method allows us reduce cost-intensive computations when number scattered data very large, as entire domain decomposed into several smaller subdomains variable radius. Numerical...

In this paper, we employ Bayesian optimization to concurrently explore the optimal values for both shape parameter and radius in partition of unity interpolation using radial basis functions. is a probabilistic, iterative approach that models error function through progressively self-updated Gaussian process. Meanwhile, harnesses meshfree method, allowing us significantly reduce computational expenses, particularly when considering substantial number scattered data points. This reduction...

In this paper we present a new fast and accurate method for Radial Basis Function (RBF) approximation, including interpolation as special case, which enables us to effectively find the optimal value of RBF shape parameter. particular, propose statistical technique, called Bayesian optimization, that consists in modelling error function with Gaussian process, by which, through an iterative parameter is selected. The process step self-updated resulting relevant decrease search time respect...

Partition of unity methods (PUMs) on graphs represent straightforward and remarkably adaptable auxiliary techniques for graph signal processing. By relying solely the intrinsic structure, we propose generation a partition through centrality measures modularity. Subsequently, integrate PUMs with local basis function (GBF) approximation approach to achieve low-cost global interpolation schemes.

Graph signal processing benefits significantly from the direct and highly adaptable supplementary techniques offered by partition of unity methods (PUMs) on graphs. In our approach, we demonstrate generation a solely based underlying graph structure, employing an algorithm that relies exclusively centrality measures modularity, without requiring input number subdomains. Subsequently, integrate PUMs with local basis function (GBF) approximation method to develop cost-effective global...