Ahac, Alan Albert2024-07-312024-07-3119851985https://hdl.handle.net/1828/16895We present an algorithm for the LU-decomposition of M-matrices based upon Gaussian Elimination applied with a new pivoting strategy. At each step of the elimination, the pivoting strategy selects a column that is the most (column) diagonally dominant in the unreduced subma­trix and exchanges it into the pivotal column position through a symmetric permutation on the matrix. We demonstrate that this approach is well-suited to M-matrices, and can be implemented efficiently. The stability of the method is shown by providing a bound on the growth factor asso­ciated with the backward error analysis of the Gaussian Elimination algorithm. We provide background for our results by surveying the literature on M-matrices, describing characterizations of matrices of this type and noting previous work regarding the LU factorization of M-matrices. Some applications in which M-matrices occur are also given. Finally, we discuss the extension of our algorithm to a larger class of matrices known as H-matrices.58 pagesAvailable to the World Wide WebThesis