An algorithm for the inverse of a multivariate homogeneous polynomial of degreen

Abstract

Various geodetic problems (the free nonlinear geodetic boundary value problem, the computation of Gaus-Kruger coordinates or UTM coordinates, the problem of nonlinear regression) demand theinversion of an univariate, bivariate, trivariate, in generalmultivariate homogeneous polynomial of degree n. The new algorithm which is oriented towardsSymbolic Computer Manipulation is based upon the algebraic power base computation with respect toKronecker-Zehfuβ product structure leading to the solution of a system oftriangular matrix equations: Only the first row of the inverse triangular matrix has to be computed. TheSymbolic Computer Manipulation program of the GKS algorithm is available from the authors.