Combined Direct-Iterative Method for Certain M-Matrix Linear Systems

摘要

Large, sparse, irreducible singular (column diagonal dominant) M-matrices A occur in various applications including queueing networks, input-output analysis and compartmental analysis. A splitting A = M - N with the matrix M having symmetric zero structure is a regular splitting and these splittings induce a combined direct-iterative solution to Ax = 0. A sparce LU factorization of a symmetric permutation of A can be obtained using a standard symmetric ordering scheme such as minimum degree. No pivoting for stability is necessary. Splitting strategies based on a tolerance factor are also discussed and some numerical experience is given. (ERA citation 08:016981)