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Algorithms and implementation of the LUfactorizations
Updates with forward and backward transformations
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active submatrix algorithm array backward transformations Bartels-Golub basis inverse basis matrix basis representation BLTF BTRAN operations bump bump rows column counts column file column permutations column singletons columnwise compute CP-time data structures deleted double pointers efficient elimination eta-vectors etas faster fill Forrest-Tomlin update FORTRAN free space area FTRAN and BTRAN Hessenberg matrix I.S. Duff implementation incoming column infeasibilities initial INSTACK linear programming lower triangular matrix LP-problems LP-solver LU-factorization LU-update Markowitz count nonbasic nucleus number of elements number of nonzeros numerical stability optimal permutation matrices PFI-update phase pivot element pivot row pivot selection pivot sequence pivot step reduce rejected columns resp row and column row count row file row index row indices rowwise scan searching Section simplex method sparse matrices sparse representation sparsity stack subdiagonal subdiagonal elements Table test problems thesis treshold pivoting triangular factors updating methods XELIMN XMODLU XRBACK