Sparse Matrix Factorization Using Multifrontal QR and Supernodal Cholesky Methods

This paper discusses the factorization of sparse matrices. A nested dissection method is used to reorder sparse matrices, while multifrontal QR and supernodal Cholesky methods are applied to factorize them. Simulations were carried out on three groups of matrices of the same size, with each group consisting of four matrices of varying sparsities. The objectives of this study are to investigate the effect of sparsity and the performance of the factorization methods. Results show that the effects of sparsity on the parameters of the matrix groups depend on their sparsity slope. Ultimately, it is demonstrated that supernodal Cholesky factorization achieves better performance than multifrontal QR.