The matrix-restricted total least-squares problem

We present and study the matrix-restricted total least squares (MRTLS) devised to solve linear systems of the form Ax b where A and b are both subjected to noise and A has errors of the form DEC. D and C are known matrices and E is unknown. We show that the MRTLS problem amounts to solving a problem of minimizing a sum of fractional quadratic terms and a quadratic function and compare it to the related restricted TLS problem of Van Huffel and Zha [The restricted total least squares problem: formulation, algorithm, and properties, SIAM J. Matrix Anal. Appl. 12(2) (1991) 292–309.]. Finally, we present an algorithm for solving the MRTLS, which is based on a reduction to a single-variable minimization problem. This reduction is shown to have the ability of eliminating local optima points. r 2006 Elsevier B.V. All rights reserved.