ABSTRACT
So far we have been concerned with solving linear least-squares problems. Now the usually simpler problem of linear equations will be considered. Note that a program designed to solve least-squares problems will give solutions to linear equations. The residual sum of squares must be zero if the equations are consistent. While this is a useful way to attack sets of equations which are suspected to possess singular coefficient matrices, since the singular-value decomposition permits such to be identified, in general the computational cost will be too high. Therefore this chapter will examine a direct approach to solving systems of linear equations. This is a variant of the elimination method taught to students in secondary schools, but the advent of automatic computation has changed only its form, showing its substance to be solid.
