A previous paper by the authors [FH93] noted that there was a strong tendency to obtain near-repeated knots in their algorithm for least squares approximation of scattered data by multiquadric functions. In this paper we observe that this leads naturally to the inclusion of derivatives of the multiquadric basis function in the approximation, and give an algorithm for accomplishing this. A compa...

Based on the radial basis functions (RBF) and T-Trefftz solution, this paper presents a new meshless method for numerically solving various partial differential equation systems. First, the analog equation method (AEM) is used to convert the original patial differential equation to an equivalent Poisson’s equation. Then, the radial basis functions (RBF) are employed to approxiamate the inhomoge...

This paper aims to survey our recent work relating to the radial basis function (RBF) from some new views of points. In the first part, we established the RBF on numerical integration analysis based on an intrinsic relationship between the Green's boundary integral representation and RBF. It is found that the kernel function of integral equation is important to create efficient RBF. The fundame...

This work aims to numerically investigate the performance of multiquadric (MQ) radial basis function in more general formats for image reconstruction applications. Desired features, i.e., accuracy and shape parameter sensitivity, each form is compared explored. The famous Lena damaged using two levels damage: 20% 40%, a Salt-and-Pepper manner. It has been discovered this that β=3/2 produces rea...

INTRODUCTION To assess changes in renal blood flow (RBF) in human and experimental sepsis, and to identify determinants of RBF. METHOD Using specific search terms we systematically interrogated two electronic reference libraries to identify experimental and human studies of sepsis and septic acute renal failure in which RBF was measured. In the retrieved studies, we assessed the influence of ...

This paper presents mesh-free procedures for solving linear differential equations (ODEs and elliptic PDEs) based on multiquadric (MQ) radial basis function networks (RBFNs). Based on our study of approximation of function and its derivatives using RBFNs that was reported in an earlier paper (Mai-Duy, N. & Tran-Cong, T. (1999). Approximation of function and its derivatives using radial basis fu...