WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 11, 2012
On the Trivariate Polynomial Interpolation
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Abstract: This paper is concerned with the formulae for computing the coefficients of the trivariate polynomial interpolation (TPI) passing through (m+1)(n+1)(r+1) distinct points in the solid rectangular region. The TPI is formulated as a matrix equation using Kronecker product and Khatri-Rao product of the matrices and the coefficients of the TPI are computed using the generalized inverse of a matrix. In addition, the closed formulae of the coefficients of the bivariate and univariate polynomial interpolations are obtained by the use of the inverse of the Vandermonde matrix. It is seen that the trivariate polynomial interpolation can be investigated as the matrix equation and the coefficients of the TPI can be computed directly from the solution of the matrix equation. Also, it is shown that the bivariate polynomial interpolation (BPI) is the special case of the TPI when0=r. Numerical examples are represented.
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Keywords: Polynomial interpolation, trivariate polynomial, bivariate polynomial, matrix equation/font>