A Tree Model for Sparse Symmetric Indefinite Matrix Factorization
Joseph W. H. Liu · SIAM Journal on Matrix Analysis and Applications · 1988
A tree model is presented to study the sparse factorization of large symmetric indefinite matrices by the diagonal pivoting method. The basic structure uses the elimination tree of symmetric matrices and the notion of delayed elimination. The factorization process for indefinite systems can be viewed as a sequence of tree transformations based on both the structural information and numerical data values. This provides a model as a common basis to study various numerical aspects of sparse symmetric indefinite decomposition.