Incomplete Cholesky (IC) factorizations have long been an important tool in the armoury of methods for the numerical solution of large sparse symmetric linear systems Ax = b. In this talk, I will explain the use of intermediate memory (memory used in the construction of the incomplete factorization but is subsequently discarded) and show how it can significantly improve the performance of the resulting IC preconditioner. I will then focus on extending the approach to sparse symmetric indefinite systems in saddle-point form. A limited-memory signed IC factorization of the form LDLT is proposed, where the diagonal matrix D has entries +/-1. The main advantage of this approach is its simplicity as it avoids the use of numerical pivoting. Instead, a global shift strategy is used to prevent breakdown and to improve performance. Numerical results illustrate the effectiveness of the signed incomplete Cholesky factorization as a preconditioner.
