상하분해 단체법에서 수정 Forrest-Tomlin 방법의 효율적인 구현

In the implementation of the simplex method program, the representation and the maintenance of basis matrix is very important, In the experimental study, we investigates Suhl's idea in the LU factorization and LU update of basis matrix. First, the triangularization of basis matrix is implemented and its efficiency is shown. Second, various technique in the dynamic Markowitz's ordering and threshold pivoting are presented. Third, modified Forrest-Tomlin LU update method exploiting sparsity is presented. Fourth, as a storage scheme of LU factors, Gustavson data structure is explained. Fifth, efficient timing of reinversion is developed. Finally, we show that modified Forrest-Tomlin method with Gustavson data structure is superior more than 30% to the Reid method with linked list data structure.