Wavelet Domain Solution of CSRBF SLAE for Image Interpolation Using Iterative Methods

2004 ◽  
Author(s):  
Luis A. Diago ◽  
Masaki Kitago ◽  
Ichiro Hagiwara
Keyword(s):  
Radial Basis Functions ◽  
Low Frequency ◽  
Direct Methods ◽  
Image Interpolation ◽  
Iterative Solution ◽  
Basis Functions ◽  
Wavelet Domain ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Radial Basis

Radial Basis Functions (RBF) are popular for interpolating scattered data. In this context, the solution of the system of linear algebraic equations (SLAE) is the most time-consuming operation. Techniques fail with large point sets consisting of more than several thousands of points when direct methods and global support are used. In this paper we demostrate that the solution of the SLAE in the wavelet domain is suitable for the problem of image interpolation by means of Compactly-Supported Radial Basis Functions (CSRBF). The iterative solution of SLAE with highly irregular matrices cannot be accelerated by wavelet transformation and subsequent sparcification if the transformed matrix is still highly irregular. To solve the SLAE in the wavelet domain, the ordering of the samples defines the spacial relationship and the energy of the coefficients in the low frequency domain. Two sorting algorithms for the wavelet domain solution are tested and compared with the spacial solution of the SLAE. Examples of image interpolation by means of CSRBF demostrate the superiority of the solution in the wavelet domain using GMRES iterative method.

scholarly journals Numerical techniques for behavior of incompressible flow in steady two-dimensional motion due to a linearly stretching of porous sheet based on radial basis functions

2019 ◽  
Vol 8 (1) ◽  
pp. 80-93
Author(s):  
Kourosh Parand ◽  
Yasaman Lotfi ◽  
Jamal Amani Rad
Keyword(s):  
Radial Basis Functions ◽  
Basis Functions ◽  
High Rate ◽  
Algebraic Equations ◽  
Polar Fluid ◽  
Radial Basis ◽  
Residual Norm ◽  
Layer Flow ◽  
Non Linear System ◽  
Better Than

AbstractIn this paper the boundary layer flow of a micro-polar fluid due to a linearly stretching sheet which is a non-linear system two-point boundary value problem (BVP) on semi-infinite interval has been considered. This the sheets are included the suction and injection. We solve this problem by two different collecation approaches and compare their results with solution of other methods. The proposed approaches are equipped by the direct (DRBF) and indirect radial basis functions (IRBF). Direct approach (DRBF) is based on a differential process and indirect approach (IRBF) is based on an integration process. These methods reduce solution of the problem to solution of a system of algebraic equations. Numerical results and residual norm show that the IRBF performs better than the common DRBF, and has an acceptable accuracy and high rate of convergence of IRBF process.

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