HSL_MI28: an efficient and robust limited-memory incomplete Cholesky factorization code. 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.

This software is also peer reviewed by journal TOMS.

References in zbMATH (referenced in 15 articles , 1 standard article )

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  1. Chen, Chao; Liang, Tianyu; Biros, George: \textttrchol: randomized Cholesky factorization for solving SDD linear systems (2021)
  2. Daas, Hussam Al; Rees, Tyrone; Scott, Jennifer: Two-level Nyström-Schur preconditioner for sparse symmetric positive definite matrices (2021)
  3. Bellavia, Stefania; Gondzio, Jacek; Porcelli, Margherita: An inexact dual logarithmic barrier method for solving sparse semidefinite programs (2019)
  4. Scott, Jennifer A.; Tůma, Miroslav: Sparse stretching for solving sparse-dense linear least-squares problems (2019)
  5. Hook, James; Scott, Jennifer; Tisseur, Françoise; Hogg, Jonathan: A Max-plus approach to incomplete Cholesky factorization preconditioners (2018)
  6. Scott, Jennifer; Tůma, Miroslav: A Schur complement approach to preconditioning sparse linear least-squares problems with some dense rows (2018)
  7. Gould, Nicholas; Scott, Jennifer: The state-of-the-art of preconditioners for sparse linear least-squares problems (2017)
  8. Scott, Jennifer: On using Cholesky-based factorizations and regularization for solving rank-deficient sparse linear least-squares problems (2017)
  9. Scott, Jennifer; Tuma, Miroslav: Solving mixed sparse-dense linear least-squares problems by preconditioned iterative methods (2017)
  10. Scott, Jennifer; Tůma, Miroslav: Improving the stability and robustness of incomplete symmetric indefinite factorization preconditioners. (2017)
  11. Scott, Jennifer; Tuma, Miroslav: Preconditioning of linear least squares by robust incomplete factorization for implicitly held normal equations (2016)
  12. Orban, Dominique: Limited-memory LDL(^\top) factorization of symmetric quasi-definite matrices with application to constrained optimization (2015)
  13. Scott, Jennifer; Tuma, Miroslav: On positive semidefinite modification schemes for incomplete Cholesky factorization (2014)
  14. Scott, Jennifer; Tůma, Miroslav: On signed incomplete Cholesky factorization preconditioners for saddle-point systems (2014)
  15. Scott, Jennifer; Tůma, Miroslav: \textttHSL_MI28: an efficient and robust limited-memory incomplete Cholesky factorization code (2014)