An optimized conjugate gradient solution for least-squares equations

The conjugate gradient method allows the solution of least-squares equations A(u -- u₀) = B without evaluating A^-1. Storage limitations can thus be satisfied by approximating A by a sparse matrix which need not be block-diagonalized. Optimization of the method allows a satisfactory solution within 10-12 iteration steps for any sized matrix, enabling an economic use of conditional slack constraints.