It is known that interpolation with radial basis functions of the same shape can guarantee a non-singular interpolation matrix, whereas little is known when one uses various shapes. In this paper, we prove that a class of compactly supported radial basis functions are convex on a certain region; based on this local convexity and ready local geometrical property of the interpolation points, we c...

In this paper we study the method of interpolation by radial basis functions and give some error estimates in Sobolev space H(Ω) (k ≥ 1). With a special kind of radial basis function, we construct a basis in H(Ω) and derive a meshless method for solving elliptic partial differential equations. We also propose a method for computing the global data density. Mathematics subject classification: 41...

When radial basis functions (RBFs) are made increasingly flat, the interpolation error typically decreases steadily until some point when Runge-type oscillations either halt or reverse this trend. Because the most obvious method to calculate an RBF interpolant becomes a numerically unstable algorithm for a stable problem in case of near-flat basis functions, there will typically also be a separ...

This article describes a fast direct solver (i.e., not iterative) for partial hierarchically semiseparable systems. This solver requires a storage of O(N logN) and has a computational complexity of O(N logN) arithmetic operations. The numerical benchmarks presented illustrate the method in the context of interpolation using radial basis functions. The key ingredients behind this fast solver are...

Based on constrained least squares approximation and techniques from computational geometry, this paper shall provide a new approximation scheme which achieves to combine well-known features from radial basis function interpolation with recent developments concerning scattered data filtering. The suggested method is shown to be well-posed, and moreover by using local error estimates from radial...

Real-time three-dimensional (RT3D) ultrasound technique based on matrix phased array transducers is likely to become predominant for dynamic screening in cardiac and obstetric practice. With these transducers large data volumes are acquired in spherical coordinates and require resampling to be visualized in Cartesian coordinates. A fast 3D resampling method was implemented and five interpolatio...

The study develops the displacement error recovery method in a mesh free environment for finite element solution employing radial point interpolation (RPI) technique. RPI technique uses basis functions (RBF), along with polynomials to interpolate fields node patch and recovers field. global local errors are quantified both energy L2 norms from post-processed considers multi-quadrics/gaussian/th...