The Solution of Overdetermined Linear Equations as a Multistage Process

The concepts of dynamic programming and multistage process theory are used to determine an analytic, least-squares solution to overdetermined linear algebraic equations. The method requires the calculation of a secondary system matrix which, together with the primary matrix, makes evident the relative dependence of the system equations. It is shown that the minimum-sum-square residual, a measure of the fit of the solution, can be determined without explicit calculation of the solution.