Interpolasi Multinomial Lagrange di Rn dan Implementasinya dalam MATLAB®

Abstract

Interpolation is a method to construct a function which goes through a given set of data points. Interpolation is usually implemented in two dimensions. Polynomial Lagrange interpolation is one of formulas that used in R². The purposes of this research are to develop the multinomial Lagrange formula in Rn by reconstructing polynomial Lagrange formula and to build an algorithm of multinomial Lagrange in R³ and its implementation. Systems of linear equations are used as illustration in a process of reconstructing polynomial Lagrange formula. The Vandermonde matrix V is the coefficient matrix of the system. The column vectors of the solution of system are coefficients of interpolation function. A method to reconstruct polynomial Lagrange formula is developed by substituting the rows of Vandermonde matrix V with monomial basis. This method is the basic of construction of multinomial Lagrange interpolation in R". The method is applied by adapting the basis used which is a multinomial basis. An algorithm of multinomial Lagrange interpolation in R³ has been constructed and implemented using MATLAB®. The result of the computation shows that the algorithm is able to work properly.