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We have recently presented a competitive method to solve overdetermined linear systems of equations with multiple right hand side vectors, where the unknown matrix is symmetric and positive definite. The coefficient and the right hand side matrices are respectively named as data and target matrices. There are also physical contexts, such as modeling a deformable structure and computing the correlation matrix in finance or insurance/reinsurance industries, where a symmetric positive semi-definite solution of an overdetermined linear system of equations needs to be computed. Several methods have been proposed for solving such problems with the assumption that the data matrix is unrealistically error free. In real measurements, however, both the data and target matrices may contain error. Thus, for practical purposes, an error in variables model appears to be more appropriate. Here, we define a new error function to consider error in both data and target matrices and propose an iterative algorithm to minimize the defined error. We illustrate that our proposed approach turns to be efficient in attaining accurate solutions. For this purpose, we generate random test problems and show that our proposed algorithm computes the solution faster than the existing methods. Moreover, the standard deviation in error matrix is considerably lower when we use our proposed algorithm. This feature makes our method more efficient and desirable in real applications.

A New Error in Variables Model for Solving Positive Semi-Definite Linear Systems with Applications to Well-known Control Problems