In this paper, an adaptive physics-based method is developed for solving wave motion problems in one dimension (i.e., wave propagation in strings, rods and beams). The solution of the problem includes two main parts. In the first part, after discretization of the domain, a physics-based method is developed considering the conservation of mass and the balance of momentum. In the second part, ada...

Abstract. We construct a new adaptive algorithm for radial basis functions (RBFs) method applied to interpolation, boundary-value, and initialboundary-value problems with localized features. Nodes can be added and removed based on residuals evaluated at a finer point set. We also adapt the shape parameters of RBFs based on the node spacings to prevent the growth of the conditioning of the inter...

Interlaced-to-progressive algorithms are currently required by video format conversion systems in order to display a progressive scanning used in modern visualization equipments. Deinterlacing algorithms use interpolation techniques to calculate missing pixels in transmitted fields. A motion adaptive algorithm which employs fuzzy logic to adapt the interpolation strategy to the presence of moti...

In this paper, an image resolution enhancing technique is described. It is based on extracting 1-dimensional characteristic curves from subsequent frames and sub-pixel displacement values. Through sub-pixel mapping and adaptive interpolation, high-resolution image can be obtained from several lowresolution image frames. This 1-dimensional algorithm is simple and cost-effective, and can be easil...

This paper describes a new result on a wavelet scheme for scattered data interpolation extensively described in [2]. The interpolation scheme of [2] already has several advantages as compared to more classical RBF: it is highly stable and highly adaptive. In this paper, we describe a new property of this scheme: that the approximation error locally only depends on a local sample density or fill...

This invited contribution first reviews basic features of multivariate interpolation by radial basis functions, before selected of its advanced topics are addressed, including recent results concerning local polyharmonic spline interpolation. The latter is one main ingredient of a novel class of adaptive meshfree semi-Lagrangian methods for transport problems. The construction of these particle...