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Direct Linear Solvers

We are considering the direct solution of the linear system

 

where A is an sparse matrix. The sparse matrix A can be numerically factored into two separate triangular matrices, one sparse matrix being lower triangular, L, and the other sparse matrix being upper triangular, U:

 

A lower triangular matrix, L, has all zeros above the diagonal and an upper triangular matrix, U, has all zeros below the diagonal [9].





David P. Koester
Sun Oct 22 15:31:10 EDT 1995