ANALYSIS OF THE GENERALIZED TOTAL LEAST-SQUARES PROBLEM AX-APPROXIMATE-TO-B WHEN SOME COLUMNS OF A ARE FREE OF ERROR

This paper studies the algebraic properties and perturbation theory of the generalized total least squares problem (GTLS) AX almost-equal-to B, in which A = (A1, A2), A, is free of error, and the error containe d in (A2, B) is of the form EC with C a given nonsingular matrix. The problem was proposed by Van Huffel and Vandewalle in [15]. The solvabi lity conditions, formulas for the GTLS solutions, their residuals, and the minimum norm correction matrices are obtained and a perturbation theory for the GTLS problem is given.