Direct Methods for Solving Sparse Systems of Linear Equations
Iain Duff · SIAM Journal on Scientific and Statistical Computing · 1984
We survey algorithms and software for solving sparse systems of linear equations by matrix factorization, paying particular attention to recent developments. We classify the various algorithms according to the type of system they solve (i.e. unsymmetric, symmetric definite, symmetric indefinite, unsymmetric but with symmetric pattern) and whether they perform pivoting for numerical stability. We consider both algorithms which work in main memory and those which use auxiliary storage. We illustrate the performance of the major approaches which we discuss by runs on test problems.