A node-addition model for symbolic factorization

Abstract

A symbolic node-addition model for matrix factorization of symmetric positive definite matrices is described. In this model, the nodes are added onto the filled graph one at a time. The advantage of the node-addition model is its simplicity and flexibility. The model can be immediately incorporated into finite element analysis programs. The model can also be extended to determine modification patterns in the matrix factors due to changes in the original matrix. For a given matrix K (= LDL t ), the time complexity of the algorithm for constructing the structure of the lower triangular matrix factor L is O (η( L )) where η( L ) is the number of nonzero entries in L .