MA57

MA57 - a code for the solution of sparse symmetric definite and indefinite systems. We introduce a new code for the direct solution of sparse symmetric linear equations that solves indefinite systems with 2 x 2 pivoting for stability. This code, called MA57, is in HSL 2002 and supersedes the well used HSL code MA27. We describe some of the implementation details and emphasize the novel features of MA57. These include restart facilities, matrix modification, partial solution for matrix factors, solution of multiple right-hand sides, and iterative refinement and error analysis. The code is written in Fortran 77, but there are additional facilities within a Fortran 90 implementation that include the ability to identify and change pivots. Several of these facilities have been developed particularly to support optimization applications, and we illustrate the performance of the code on problems arising therefrom.

This software is also peer reviewed by journal TOMS.


References in zbMATH (referenced in 74 articles , 1 standard article )

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  1. Birgin, E. G.; Martínez, J. M.: A Newton-like method with mixed factorizations and cubic regularization for unconstrained minimization (2019)
  2. Kuřátko, Jan: Factorization of saddle-point matrices in dynamical systems optimization -- reusing pivots (2019)
  3. Arreckx, Sylvain; Orban, Dominique: A regularized factorization-free method for equality-constrained optimization (2018)
  4. Druinsky, Alex; Carlebach, Eyal; Toledo, Sivan: Wilkinson’s inertia-revealing factorization and its application to sparse matrices. (2018)
  5. Huber, Andreas; Gerdts, Matthias; Bertolazzi, Enrico: Structure exploitation in an interior-point method for fully discretized, state constrained optimal control problems (2018)
  6. Nicholson, Bethany L.; Wan, Wei; Kameswaran, Shivakumar; Biegler, Lorenz T.: Parallel cyclic reduction strategies for linear systems that arise in dynamic optimization problems (2018)
  7. Rees, Tyrone; Scott, Jennifer: A comparative study of null-space factorizations for sparse symmetric saddle point systems. (2018)
  8. Scott, Jennifer; Tůma, Miroslav: A Schur complement approach to preconditioning sparse linear least-squares problems with some dense rows (2018)
  9. Steffen, Kyle R.; Epshteyn, Yekaterina; Zhu, Jingyi; Bowler, Megan J.; Deming, Jody W.; Golden, Kenneth M.: Network modeling of fluid transport through sea ice with entrained exopolymeric substances (2018)
  10. Webert, Jan-Hendrik; Gill, Philip E.; Kimmerle, Sven-Joachim; Gerdts, Matthias: A study of structure-exploiting SQP algorithms for an optimal control problem with coupled hyperbolic and ordinary differential equation constraints (2018)
  11. Armand, Paul; Omheni, Riadh: A mixed logarithmic barrier-augmented Lagrangian method for nonlinear optimization (2017)
  12. Carson, Erin; Higham, Nicholas J.: A new analysis of iterative refinement and its application to accurate solution of ill-conditioned sparse linear systems (2017)
  13. Gould, Nicholas I. M.; Robinson, Daniel P.: A dual gradient-projection method for large-scale strictly convex quadratic problems (2017)
  14. Gould, Nicholas; Scott, Jennifer: The state-of-the-art of preconditioners for sparse linear least-squares problems (2017)
  15. Huang, Kuo-Ling; Mehrotra, Sanjay: Solution of monotone complementarity and general convex programming problems using a modified potential reduction interior point method (2017)
  16. Koehler, Sarah; Danielson, Claus; Borrelli, Francesco: A primal-dual active-set method for distributed model predictive control (2017)
  17. Orban, Dominique; Arioli, Mario: Iterative solution of symmetric quasi-definite linear systems (2017)
  18. Pecci, Filippo; Abraham, Edo; Stoianov, Ivan: Penalty and relaxation methods for the optimal placement and operation of control valves in water supply networks (2017)
  19. Scott, Jennifer: On using Cholesky-based factorizations and regularization for solving rank-deficient sparse linear least-squares problems (2017)
  20. Suñagua, Porfirio; Oliveira, Aurelio R. L.: A new approach for finding a basis for the splitting preconditioner for linear systems from interior point methods (2017)

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