Bivariate Interpolation in Triangular Form

The purpose of this paper is to derive lagrange interpolation formula for a single variable and two independent variables in triangular form. Firstly, single variable interpolation is derived and then two independent variable interpolation derived in triangular form. In this paper, we derived the formula of three points of fit approximation, six points of fit approximation and ten points of fit approximation with their examples respectively. And also derived the approximation using a general triangular form of points with examples.

Bivariate Interpolation in Rectangular Form

The purpose of this paper is to derive lagrange interpolation formula for a single variable and two independent variables. Firstly, single variable interpolation is derived and then two independent variable interpolation derived. Some practical problems are computed by virtue of these interpolation formula.

CONSTRUCTION OF RECURRENT FRACTAL INTERPOLATION SURFACES WITH FUNCTION SCALING FACTORS AND ESTIMATION OF BOX-COUNTING DIMENSION ON RECTANGULAR GRIDS

We consider a construction of recurrent fractal interpolation surfaces (RFISs) with function vertical scaling factors and estimation of their box-counting dimension. A RFIS is an attractor of a recurrent iterated function system (RIFS) which is a graph of bivariate interpolation function. For any given dataset on rectangular grids, we construct general RIFSs with function vertical scaling factors and prove the existence of bivariate functions whose graph are attractors of the above-constructed RIFSs. Finally, we estimate lower and upper bounds for the box-counting dimension of the constructed RFISs.

Convergence of Bivariate Interpolation and its Computation

The problem constructed here is the convergence of bivariate trigonometric interpolation sequences, the approximation and computation would be optimal for a body of functions. Therefore some conclusions became a special cased of the results of present paper.

A New Approach to General Interpolation Formulae for Bivariate Interpolation

General interpolation formulae for bivariate interpolation are established by introducing multiple parameters, which are extensions and improvements of those studied by Tan and Fang. The general interpolation formulae include general interpolation formulae of symmetric branched continued fraction, general interpolation formulae of univariate and bivariate interpolation, univariate block based blending rational interpolation, bivariate block based blending rational interpolation and their dual schemes, and some interpolation form studied by many scholars in recent years. We discuss the interpolation theorem, algorithms, dual interpolation, and special cases and give many kinds of interpolation scheme. Numerical examples are given to show the effectiveness of the method.