Matrix rank/inertia formulas for least-squares solutions with statistical applications

Matrix rank/inertia formulas for least-squares solutions with statistical applications

Least-Squares Solution (LSS) of a linear matrix equation and Ordinary Least-Squares Estimator (OLSE) of unknown parameters in a general linear model are two standard algebraical methods in computational mathematics and regression analysis. Assume that a symmetric quadratic matrix-valued function φ(Z) = Q − ZPZ′ is given, where Z is taken as the LSS of the linear matrix equation AZ = B. In this ...

Least Squares Solutions of Inconsistent Fuzzy Linear Matrix Equations

least squares solutions of inconsistent fuzzy linear matrix equations

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least squares solutions of inconsistent fuzzy linear matrix equations

Iterative least-squares solutions of coupled Sylvester matrix equations

In this paper, we present a general family of iterative methods to solve linear equations, which includes the well-known Jacobi and Gauss–Seidel iterations as its special cases. The methods are extended to solve coupled Sylvester matrix equations. In our approach, we regard the unknown matrices to be solved as the system parameters to be identified, and propose a least-squares iterative algorit...