Implicit iterative algorithm for solving regularized total least squares problems

Abstract

The article considers a new iterative algorithm for solving total least squares problems. A new version of the implicit method of simple iterations based on singular value decomposition is proposed for solving a biased normal system of algebraic equations. The use of the implicit method of simple iterations based on singular value decomposition makes it possible to replace an ill-conditioned problem with a sequence of problems with a smaller condition number. This makes it possible to significantly increase the computational stability of the algorithm and, at the same time, ensures its high rate of convergence. Test examples shown that the proposed algorithm has a higher accuracy compared to the solutions obtained by non-regularized total least squares algorithms, as well as the total least squares solution with Tikhonov regularization.

Keywords

• implicit regularization
• total least squares
• singular value decomposition
• ill-conditioning
• iterative regularization methods