Minimax Estimation of Solutions of Systems of Linear Algebraic Equations with Singular Matrices
Sergey N. Zhuk · Journal of Automation and Information Sciences · 2004
Minimax estimations of sets of solutions of a system of linear algebraic equations with rectangular matrices, optimal in mean-square sense, are derived. Corresponding representations for derived estimates are constructed in terms of pseudoinverse matrices. In particular, for the case of nondegenerate matrices it is demonstrated, that the suggested estimates coincide with the corresponding minimax estimates of solutions of a system of linear algebraic equations with square nondegenerate matrices.