APPROXIMATING SURFACES BY MOVING TOTAL LEAST-SQUARES METHOD

We suggest a method for generating a surface approximating the given d ata (x(i), y(i), z(i)) is an element of [R-3, i = 1..., m, assuming th at the errors can occur both in the independent variables x and y, as well as in the dependent variable z. Our approach is based on the movi ng total least squares method, where the local approximants (local pla nes) are determined in the sense of total least squares. The parameter s of the local approximants are obtained by finding the eigenvector, c orresponding to the smallest eigenvalue of a certain symmetric matrix. To this end, we develop a procedure based on the inverse power method . The method is tested on several examples. (C) 1998 Elsevier Science Inc. All rights reserved.