An efficient Gauss-Newton algorithm for solving regularized total least squares problems

The total least squares (TLS) method is a well-known technique for solving an overdetermined linear system of equations Ax approximate to b, that is appropriate when both the coefficient matrix A and the right-hand side vector b are contaminated by some noise. For ill-posed TLS poblems, regularization techniques are necessary to stabilize the computed solution; otherwise, TLS produces a noise-dominant output. In this paper, we show that the regularized total least squares (RTLS) problem can be reformulated as a nonlinear least squares problem and can be solved by the Gauss-Newton method. Due to the nature of the RTLS problem, we present an appropriate method to choose a good regularization parameter and also a good initial guess. Finally, the efficiency of the proposed method is examined by some test problems.

Automated summary

This paper presents how the regularized total least squares (RTLS) problem can be reformulated as a nonlinear least squares problem and solved using the Gauss-Newton method. The method also includes a strategy for selecting a good regularization parameter and initial guess. The efficiency of the proposed method is validated through test problems.