The interpolation by polynomials or other functions is a rather old method in applied mathematics. In the paper of M. Gasca and T. Sauer [9] it is mentioned that the word ''interpolation'' has apparently been introduced by J.Wallis as early as 1655. Compared to this, polynomial interpolation in several variables is a relatively new topic and it probably only started in the second half of 19 cen...

‎In this paper‎, ‎firstly‎, ‎we review approximation of fuzzy functions‎ ‎by fuzzy bicubic splines interpolation and present a new approach‎ ‎based on the two-dimensional fuzzy splines interpolation and‎ ‎iterative method to approximate the solution of two-dimensional‎ ‎linear fuzzy Fredholm integral equation (2DLFFIE)‎. ‎Also‎, ‎we prove‎ ‎convergence analysis and numerical stability analysis ...

In this paper, we applied the support vector machine (SVM) to the spatial interpolation of the multi-year average annual precipitation in the Three Gorges Region basin. By combining it with the inverse distance weighting and ordinary kriging method, we constructed the SVM residual inverse distance weighting, as well as the SVM residual kriging precipitation interpolation model and compared them...

Image interpolation is a procedure used in expanding and contracting digital images. Image interpolation is referred by various terminologies such as image scaling, image resizing, image resampling, digital zooming, image magnification or enhancement. Image interpolation is widely used in many consumer application devices such as charge-coupled device (CCD) camera, closed circuit television (CC...

In this paper a general theory for interpolation methods on a rectangular grid is introduced. By the use of this theory an efficient B-spline-based interpolation method for spectral codes is presented. The theory links the order of the interpolation method with its spectral properties. In this way many properties like order of continuity, order of convergence, and magnitude of errors can be exp...

Spatial interpolation is an important feature of a Geographic Information System, which is the procedure used to estimate values at unknown locations within the area covered by existing observations. In this paper, we propose a conservative spatial interpolation technique that incorporates the advantages of local interpolation, Euclidean interpolation, and conservative fuzzy reasoning. The main...

Properties of the hybrid of block-pulse functions and Lagrange polynomials based on the Legendre-Gauss-type points are investigated and utilized to define the composite interpolation operator as an extension of the well-known Legendre interpolation operator. The uniqueness and interpolating properties are discussed and the corresponding differentiation matrix is also introduced. The appl...

Image magnification algorithms directly affect the quality of image magnification. In this paper, based on the image interpolation algorithm principle, features of the nearest neighbor interpolation, bilinear interpolation, bicubic interpolation and cubic B spline interpolation were analyzed. At the same time, their advantages and disadvantages were compared. In the experiment, image magnificat...

We present a solution for the classical univariate rational interpolation problem by means of (univariate) subresultants. In the case of Cauchy interpolation (interpolation without multiplicities), we give explicit formulas for the solution in terms of symmetric functions of the input data, generalizing the well-known formulas for Lagrange interpolation. In the case of the osculatory rational i...

Interpolation is one of the widely used in many applications Image processing such as scaling, re-sampling and re-targeting. The Interpolation which estimates unknown target pixel value from surrounding neighborhood known pixels, the quality of Interpolation algorithm depends on number of pixels used in estimation. An image consists of edge and smooth pixels. Hence To exploiting content of the ...