THE PARAMETRIC QUADRATIC FORM METHOD FOR SOLVING TLS PROBLEMS WITH ELEMENTWISE WEIGHTING

This paper considers the Total Least Squares (TLS) problem with Elementwise Weighting (EW), removing the assumption of identical variances of data and observation errors while preserving their statistical independence. To solve them we approximate the gradient of the weighted Frobenius norm of errors by the gradient of an ad hoc Parametric Quadratic Form and present a fast iterative algorithm, exhibiting quadratic convergence. Some numerical examples show the capabilities of this algorithm in solving EW-TLS problems.