in this paper, an effective and simple numerical method is proposed for solving systems of integral equations using radial basis functions (rbfs). we present an algorithm based on interpolation by radial basis functions including multiquadratics (mqs), using legendre-gauss-lobatto nodes and weights. also a theorem is proved for convergence of the algorithm. some numerical examples are presented...

Radial Basis Functions (RBF) interpolation theory is briefly introduced at the “application level” including some basic principles and computational issues. The RBF interpolation is convenient for un-ordered data sets in n-dimensional space, in general. This approach is convenient especially for a higher dimension N 2 conversion to ordered data set, e.g. using tessellation, is computationally v...

It is shown that a theorem of E. Rakotch for locally contractive mappings can be deduced from Banach's contraction mapping theorem, and a counterexample to an assertion of R. D. Holmes concerning local radial contractions is given. Let (X, d) be a metric space, k G (0, 1), and g a mapping of X into X. If for each x G X there exists a neighborhood A^(x) of x such that for each u, v G N(x), d(g(u...

The classical radial point interpolation method (RPIM) is a powerful meshfree numerical technique for engineering computation. In the original RPIM, moving support domain quadrature usually employed field function approximation, but local supports of nodal shape functions are always not in alignment with integration cells constructed integration. This misalignment can result additional error an...

Symmetric collocation, which can be used to numerically solve linear partial differential equations, is a natural generalization of the well-established scattered data interpolation method known as radial basis function (rbf) interpolation. As with rbf interpolation, a major shortcoming of symmetric collocation is the high cost, in terms of floating point operations, of evaluating the obtained ...

Approximation and Interpolation Employing Divergence–free Radial Basis Functions with Applications. (May 2002) Svenja Lowitzsch, Dipl., Georg-August University, Göttingen Co–Chairs of Advisory Committee: Dr. Francis J. Narcowich Dr. Joseph D. Ward Approximation and interpolation employing radial basis functions has found important applications since the early 1980’s in areas such as signal proc...

For interpolation of scattered multivariate data by radial basis functions, an \uncertainty relation" between the attainable error and the condition of the interpolation matrices is proven. It states that the error and the condition number cannot both be kept small. Bounds on the Lebesgue constants are obtained as a byproduct. A variation of the Narcowich{Ward theory of upper bounds on the norm...

This paper deals with some basic aspects of scattered data problems. In particular, the following topics are discussed: Self-adjoint scattered data interpolation, sampling sets and interpolation sets, and irregular sampling of shift-invariant spline spaces. Results on band-limited functions are presented as well as results on univariate splines on the real line. x0. Introduction Scattered data ...

It is often observed that interpolation based on translates of radial basis functions or non-radial kernels is numerically unstable due to exceedingly large condition of the kernel matrix. But if stability is assessed in function space without considering special bases, this paper proves that kernel–based interpolation is stable. Provided that the data are not too wildly scattered, the L2 or L∞...