HSL_MI28

This article focuses on the design and development of a new robust and efficient general-purpose incomplete Cholesky factorization package HSL_MI28, which is available within the HSL mathematical software library. It implements a limited memory approach that exploits ideas from the positive semidefinite Tismenetsky-Kaporin modification scheme and, through the incorporation of intermediate memory, is a generalization of the widely used ICFS algorithm of Lin and Moré. Both the density of the incomplete factor and the amount of memory used in its computation are under the user's control. The performance of HSL_MI28 is demonstrated using extensive numerical experiments involving a large set of test problems arising from a wide range of real-world applications. The numerical experiments are used to isolate the effects of scaling, ordering, and dropping strategies so as to assess their usefulness in the development of robust algebraic incomplete factorization preconditioners and to select default settings for HSL_MI28. They also illustrate the significant advantage of employing a modest amount of intermediate memory. Furthermore, the results demonstrate that, with limited memory, high-quality yet sparse general-purpose preconditioners are obtained. Comparisons are made with ICFS, with a level-based incomplete factorization code and, finally, with a state-of-the-art direct solver.