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 83 articles , 1 standard article )

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  1. Hogg, J. D.; Scott, J. A.: A fast and robust mixed-precision solver for the solution of sparse symmetric linear systems (2010)
  2. Liu, Shu-Tian; Luo, Xin-Long: A method based on Rayleigh quotient gradient flow for extreme and interior eigenvalue problems (2010)
  3. Naumov, Maxim; Manguoglu, Murat; Sameh, Ahmed H.: A tearing-based hybrid parallel sparse linear system solver (2010)
  4. Scott, Jennifer A.: Scaling and pivoting in an out-of-core sparse direct solver (2010)
  5. Arioli, M.; Duff, I. S.: Using FGMRES to obtain backward stability in mixed precision (2009)
  6. Duff, Iain S.: The design and use of a sparse direct solver for skew symmetric matrices (2009)
  7. Janna, Carlo; Comerlati, Andrea; Gambolati, Giuseppe: A comparison of projective and direct solvers for finite elements in elastostatics (2009)
  8. Reid, J. K.; Scott, J. A.: An efficient out-of-core multifrontal solver for large-scale unsymmetric element problems (2009)
  9. Zavala, Victor M.; Biegler, Lorenz T.: Nonlinear programming strategies for state estimation and model predictive control (2009)
  10. Friedlander, Michael P.; Leyffer, Sven: Global and finite termination of a two-phase augmented Lagrangian filter method for general quadratic programs (2008)
  11. Gould, Nicholas I. M.: How good are projection methods for convex feasibility problems? (2008)
  12. Fritzsche, David; Frommer, Andreas; Szyld, Daniel B.: Extensions of certain graph-based algorithms for preconditioning (2007)
  13. Schenk, Olaf; Wächter, Andreas; Hagemann, Michael: Matching-based preprocessing algorithms to the solution of saddle-point problems in large-scale nonconvex interior-point optimization (2007)
  14. Dollar, H. Sue; Gould, Nicholas I. M.; Schilders, Wil H. A.; Wathen, Andrew J.: Implicit-factorization preconditioning and iterative solvers for regularized saddle-point systems (2006)
  15. Dollar, H. Sue; Gould, Nicholas I. M.; Wathen, Andrew J.: On implicit-factorization constraint preconditioners (2006)
  16. Duff, Iain S.; Pralet, Stéphane: Strategies for scaling and pivoting for sparse symmetric indefinite problems (2005)
  17. Oliveira, A. R. L.; Sorensen, D. C.: A new class of preconditioners for large-scale linear systems from interior point methods for linear programming (2005)
  18. Duff, Iain S.: MA57 -- a code for the solution of sparse symmetric definite and indefinite systems (2004)
  19. Gould, Nicholas I. M.; Scott, Jennifer A.: A numerical evaluation of HSL packages for the direct solution of large sparse, symmetric linear systems of equations (2004)
  20. Wills, Adrian G.; Heath, William P.: Barrier function based model predictive control (2004)