B-splines provide an accurate and efficient method for interpolating regularly spaced data. In this paper, I study the applicability of B-spline interpolation in the context of the inverse interpolation method for regularizing irregular data. Numerical tests show that, in comparison with lower-order linear interpolation, B-splines lead to a faster iterative conversion in under-determined proble...

We consider the interpolation problem for functions whose range and whose domain both consist of convex or fuzzy subsets of a real Euclidean space. This problem arises in fuzzy controlling, namely when the functional dependence between two fuzzy vectors is known only for finitely many cases. To have a criterion for an appropriate choice of an interpolation function, we generalise the well-known...

Spectral factorization is a computational procedure for constructing minimumphase (stable inverse) filters required for recursive inverse filtering. We present a novel method of spectral factorization. The method iteratively constructs an approximation of the minimum-phase filter with the given autocorrelation by repeated forward and inverse filtering and rearranging the terms. This procedure i...

(1) 1 we obtained analytical expressions for the kernel (22) and cross-kernel (23). We have used these kernels for solving the corresponding regression problem and reconstructing images based on data that is similar to what one might get from a Positron Emission Tomography scan Shepp, Vardi & Kaufman, 1985]. A remarkable feature of this solution is that it avoids a pixel representation of the f...

In this work, we introduce a novel method for solving two-dimensional fuzzy Fredholm integral equations of the second kind (2D-FFIE-2). We use new representation of parametric form of fuzzy numbers and convert a two-dimensional fuzzy Fredholm integral equation to system of two-dimensional Fredholm integral equations of the second kind in crisp case. We can use Adomian decomposition method for n...

in this paper, rst a design is proposed for representing fuzzy polynomials withinput fuzzy and output fuzzy. then, we sketch a constructive proof for existenceof such polynomial which can be fuzzy interpolation polynomial in a set given ofdiscrete points rather than a fuzzy function. finally, to illustrate some numericalexamples are solved.

Two forms of spatial interpolation, the interpolation of point and areal data, are distinguished. Traditionally, point interpolation is applied to isarithmic, that is, contour mapping and areal interpolation to isopleth mapping. Recently, areal interpolation techniques have been used to obtain data for a set of administrative or political districts from another set of districts whose boundaries...

Experimental and computational data field obtained from measurements are often sparse noisy. Consequently, interpolating unknown functions under these restrictions to provide accurate predictions is very challenging. This study compares machine-learning methods cubic splines on the sparsity of training they can handle, especially when samples We compare deviation a true function f using mean sq...

This work introduces a reduced order modeling (ROM) framework for the solution of parameterized second-order linear elliptic partial differential equations formulated on unfitted geometries. The goal is to construct efficient projection-based ROMs, which rely techniques such as basis method and discrete empirical interpolation. presence geometrical parameters in domain discretizations entails c...