The multifrontal method is a direct method for solving systems of linear equations Ax = b, when A is a sparse matrix and x and b are vectors or matrices. The multifrontal method organizes the operations that take place during the factorization of sparse matrices in such a way that the entire factorization is performed through partial factorizations of a sequence of dense and small submatrices. It is guided by a tree that represents the dependencies between those partial factorizations. In the following, the multifrontal method is formulated first for finite-element analysis and later generalized to assembled sparse matrices.
The Multifrontal Method
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