We consider the problem of computing solutions to a variety of matrix rational interpolation problems. These include the partial realization problem for matrix power series and Newton-Pad e, Hermite-Pad e, Simultaneous Pad e, M-Pad e and multipoint Pad e approximation problems along with their matrix generalizations. A general recurrence relation is given for solving these problems. Unlike othe...

Since the works of Newton and Lagrange, interpolation had been a mature technique in the numerical mathematics. Among the many interpolation methods, global or piecewise, the polynomial interpolation p(x) = a0 +a1x+ . . .+ anx expanded by the monomials is the simplest one, which is easy to handle mathematically. For higher accuracy, one always attempts to use a higher-order polynomial as an int...

The scheme of divided differences is widely used in many approximation and interpolation problems. Computing the Newton coefficients of the interpolating polynomial is the first step of the Björck and Pereyra algorithm for solving Vandermonde systems of equations (Cf. [1]). Very often this algorithm produces very accurate solution. The problem of determining the Newton coefficients is intimatel...

In this paper, according to the development of the fractional differentiation and its applications in the modern signal processing, we improve the numerical calculation of fractional differentiation by Newton interpolation equation, and propose a new mask, the Newton Interpolation’s Fractional Differentiation (NIFD). Then, we apply this new mask to image edge detection and can obtain the better...

In this paper we present a new method for accelerating ray tracing of scenes containing NURBS (Non Uniform Rational B-Spline) surfaces by exploiting the GPU’s fast z-buffer rasterization for regular triangle meshes. In combination with a lightweight, memory efficient data organization this allows for fast calculation of primary ray intersections using a Newton Iteration based approach executed ...

In this paper, we study iterative methods on the coefficients of the rational univariate representation (RUR) of a given algebraic set, called global Newton iteration. We compare two natural approaches to define locally quadratically convergent iterations: the first one involves Newton iteration applied to the approximate roots individually and then interpolation to find the RUR of these approx...

In this paper, we study iterative methods on the coefficients of the rational univariate representation (RUR) of a given algebraic set, called global Newton iteration. We compare two natural approaches to define locally quadratically convergent iterations: the first one involves Newton iteration applied to the approximate roots individually and then interpolation to find the RUR of these approx...

In this paper, a general family of n-point Newton type iterative methods for solving nonlinear equations is constructed by using direct Hermite interpolation. The order of convergence of the new n-point iterative methods without memory is 2 requiring the evaluations of n functions and one first-order derivative in per full iteration, which implies that this family is optimal according to Kung a...

A new method for computing the approximation of bivariate matrix function is introduced. It uses the construction of bivariate Newton-Thiele type matrix rational interpolants on a rectangular grid.The rational interpolant is of the formmotivated by Tan and Fang (2000), which is combined by Newton interpolant and branched continued fractions, with scalar denominator. The matrix quotients are bas...

High-efficiency and high-accuracy deformation analysis using digital image correlation (DIC) has become increasingly important in recent years, considering the ongoing trend of using higher resolution digital cameras and common requirement of processing a large sequence of images recorded in a dynamic testing. In this work, to eliminate the redundant computations involved in conventional DIC me...