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, Jonathan D.; Scott, Jennifer A.: Pivoting strategies for tough sparse indefinite systems (2013)
  2. Hogg, Jonathan D.; Scott, Jennifer A.: An efficient analyse phase for element problems. (2013)
  3. Hogg, Jonathan; Scott, Jennifer: New parallel sparse direct solvers for multicore architectures (2013)
  4. Lubin, Miles; Martin, Kipp; Petra, Cosmin G.; Sandıkçı, Burhaneddin: On parallelizing dual decomposition in stochastic integer programming (2013)
  5. Pascon, J. P.; Coda, H. B.: Large deformation analysis of elastoplastic homogeneous materials via high order tetrahedral finite elements (2013)
  6. Pascon, J. P.; Coda, H. B.: High-order tetrahedral finite elements applied to large deformation analysis of functionally graded rubber-like materials (2013)
  7. Patterson, Michael A.; Weinstein, Matthew; Rao, Anil V.: An efficient overloaded method for computing derivatives of mathematical functions in MATLAB (2013)
  8. Blank, Luise; Sarbu, Lavinia; Stoll, Martin: Preconditioning for Allen-Cahn variational inequalities with non-local constraints (2012)
  9. Gill, Philip E.; Wong, Elizabeth: Sequential quadratic programming methods (2012)
  10. Toh, Kim-Chuan; Todd, Michael J.; Tütüncü, Reha H.: On the implementation and usage of SDPT3 -- a Matlab software package for semidefinite-quadratic-linear programming, version 4.0 (2012)
  11. Duff, Iain; Mijuca, Dubravka: On accurate and time efficient solution of primal-mixed finite element equations in multiscale solid mechanics (2011)
  12. Kirches, Christian: Fast numerical methods for mixed-integer nonlinear model-predictive control (2011)
  13. Kirches, Christian; Bock, Hans Georg; Schlöder, Johannes P.; Sager, Sebastian: A factorization with update procedures for a KKT matrix arising in direct optimal control (2011)
  14. Kirches, Christian; Bock, Hans Georg; Schlöder, Johannes P.; Sager, Sebastian: Block-structured quadratic programming for the direct multiple shooting method for optimal control (2011)
  15. Thorne, H. Sue: Distributed control and constraint preconditioners (2011)
  16. Canuto, Claudio; Gervasio, Paola; Quarteroni, Alfio: Finite-element preconditioning of G-NI spectral methods (2010)
  17. Dollar, H. S.; Scott, J. A.: A note on fast approximate minimum degree orderings for symmetric matrices with some dense rows (2010)
  18. Gould, Nicholas I. M.; Robinson, Daniel P.; Thorne, H. Sue: On solving trust-region and other regularised subproblems in optimization (2010)
  19. Gould, N. I. M.; Toint, Ph. L.: Nonlinear programming without a penalty function or a filter (2010)
  20. Hogg, J. D.; Reid, J. K.; Scott, J. A.: Design of a multicore sparse Cholesky factorization using DAGs (2010)