A Descent Method for the Uniform Solution to Over-Determined Systems of Linear Equations

Given a system of linear equations with more equations than unknowns, we seek to determine that vector of unknowns which minimizes the norm of the residual of the system in the uniform sense. A method is presented which obtains this solution after a finite number of trial solutions have been examined in a sequence in which the residual norm decreases with each successive step. The implementation of the method exploits efficient matrix decomposition updating schemes resulting in reduced computation times when compared with a presently popular method.