Evaluation and analysis of most remotely sensed data requires careful image-to-image registration or ortho-rectification (geocoding). Photogrammetric practice has shown that polynomial transformation functions are useful for registration of aerial photographs. However, multiand hyperspectral remotely sensed data are often recorded by airborne line scanners. Then ortho-rectification by conventio...

A computational algorithm based on the multiquadric, which is a continuously diierentiable radial basis function, is devised to solve the shallow-water equations. The numerical solutions are evaluated at scattered collocation points and the spatial partial derivatives are formed directly from partial derivatives of the radial basis function, not by any diierence scheme. The method does not requ...

This paper discusses the application of the multi-zone decomposition technique with Multiquadric scheme for the numerical solutions of a time-dependent problem. The construction of the multi-zone algorithm is based on a domain decomposition technique to subdivide the global region into a number of nite subdomains. The reduction of ill-conditioning and the improvement of the computational eecien...

Over the past decade, the radial basis function method has been shown to produce high quality solutions to the multivariate scattered data interpolation problem. However, this method has been associated with very high computational cost, as compared to alternative methods such as finite element or multivariate spline interpolation. For example, the direct evaluation at M locations of a radial b...

Radial basis function methods for interpolation can be interpreted as roughness-minimizing splines. Although this relationship has already been established for radial basis functions of the form g(r) = r and g(r) = r log(r), it is extended here to include a much larger class of functions. This class includes the multiquadric g(r) = (r 2 + c 2) 1=2 and inverse multiquadric g(r) = (r 2 + c 2) ?1=...

A treecode algorithm is presented for the fast evaluation of multiquadric radial basis function (RBF) approximations. The method is a dual approach to one presented by Krasny and Wang, which applies far-field expansions to clusters of RBF centers (source points). The new approach clusters evaluation points instead and is therefore easily able to cope with basis functions that have different mul...

In the 1990’s exponential-type error bounds appeared in the theory of radial basis functions. For multiquadric interpolation it is O(λ 1 d ) as d → 0, where λ is a constant satisfying 0 < λ < 1. For Gaussian interpolation it is O(C d) c′ d as d → 0 where C ′ and c are constants. In both cases the parameter d, called fill distance, measures the spacing of the points where interpolation occurs. T...

In this paper, coupled nonlinear Burgers’ equations are solved through a variety of meshless methods known as multiquadric quasi-interpolation scheme. In this scheme, the extension of univariate quasi-interpolation method is used to approximate the unknown functions and their spatial derivatives and the Taylor series expansion is used to discretize the temporal derivatives. The multiquadric qua...

Abstract. Radial basis functions (RBFs) are a powerful tool for interpolating/approximating multidimensional scattered data. Notwithstanding, RBFs pose computational challenges, such as the efficient evaluation of an n-center RBF expansion at m points. A direct summation requires O(nm) operations. We present a new multilevel method whose cost is only O((n + m) ln(1/δ)), where δ is the desired a...