MA57 swMATH ID: 536 Software Authors: Duff, Iain S. Description: 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. Homepage: http://dl.acm.org/citation.cfm?id=992202 Related Software: HSL; Ipopt; SparseMatrix; PARDISO; CUTEr; CUTEst; UMFPACK; LOQO; HSL_MA97; SifDec; Matlab; SNOPT; qpOASES; LAPACK; WSMP; METIS; GALAHAD; CHOLMOD; HSL_MA77; KNITRO Cited in: 95 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year MA57 – a code for the solution of sparse symmetric definite and indefinite systems. Zbl 1070.65525Duff, Iain S. 2004 all top 5 Cited by 152 Authors 13 Scott, Jennifer A. 9 Gould, Nicholas Ian Mark 6 Duff, Iain S. 6 Hogg, Jonathan D. 5 Orban, Dominique 4 Armand, Paul 4 Gill, Philip E. 4 Kirches, Christian 3 Biegler, Lorenz T. 3 Dollar, H. Sue 3 Gerdts, Matthias 3 Rao, Anil V. 3 Sager, Sebastian 3 Toint, Philippe L. 3 Wong, Elizabeth 2 Arioli, Mario 2 Bock, Hans Georg 2 Coda, Humberto Breves 2 Davis, Timothy Alden 2 Janka, Dennis 2 Oliveira, Aurelio Ribeiro Leite 2 Omheni, Riadh 2 Pascon, João Paulo 2 Rees, Tyrone 2 Reid, John 2 Robinson, Daniel P. 2 Schlöder, Johannes P. 2 Stoll, Martin 2 Thore, Carl-Johan 2 Thorne, H. Sue 2 Tran, Ngoc Nguyen 2 Tůma, Miroslav 2 Wächter, Andreas 2 Wan, Wei 2 Wathen, Andrew John 2 Zavala, Victor M. 1 Abraham, Edo 1 Agamawi, Yunus M. 1 Arreckx, Sylvain 1 Barker, Andrew T. 1 Benner, Peter 1 Benoist, Joël 1 Bertolazzi, Enrico 1 Birgin, Ernesto G. 1 Blank, Luise 1 Borrelli, Francesco 1 Bowler, Megan J. 1 Bueno, Luís Felipe 1 Cannataro, Begüm Şenses 1 Canuto, Claudio 1 Carlebach, Eyal 1 Carson, Erin Claire 1 Chen, Zhongwen 1 Chiang, Naiyuan 1 Chung, Hayoung 1 Comerlati, Andrea 1 Cristofari, Andrea 1 Cui, Yiran 1 Danielson, Claus 1 Deming, Jody W. 1 DiPillo, Gianni 1 Domahidi, Alexander 1 Domínguez, Víctor 1 Druinsky, Alex 1 Egidi, Nadaniela 1 Epshteyn, Yekaterina 1 Forsgren, Anders 1 Friedlander, Michael P. 1 Fritzsche, David 1 Frommer, Andreas 1 Gambolati, Giuseppe 1 Ganesh, Mahadevan 1 Gertz, E. Michael 1 Gervasio, Paola 1 Ghannad, Alexandre 1 Gioia, E. 1 Golden, Kenneth M. 1 Haeser, Gabriel 1 Hagemann, Michael 1 Hager, William W. 1 Hayami, Ken 1 Heath, William Paul 1 Higham, Nicholas J. 1 Holmberg, Erik 1 Huang, Kuo-Ling 1 Huber, Andreas 1 Janna, Carlo 1 Jerez, Juan Luis 1 Kambampati, Sandilya 1 Kameswaran, Shivakumar 1 Kim, H. Alicia 1 Kimmerle, Sven-Joachim 1 Klarbring, Anders 1 Koehler, Sarah 1 Kolmanovsky, Ilya V. 1 Kunkel, Martin 1 Kuřátko, Jan 1 Leyffer, Sven 1 Liao-McPherson, Dominic 1 Liu, Shutian ...and 52 more Authors all top 5 Cited in 36 Serials 14 Computational Optimization and Applications 11 ACM Transactions on Mathematical Software 8 SIAM Journal on Scientific Computing 4 SIAM Journal on Matrix Analysis and Applications 4 Numerical Linear Algebra with Applications 4 Mathematical Programming Computation 3 Computer Methods in Applied Mechanics and Engineering 3 Journal of Optimization Theory and Applications 3 Linear Algebra and its Applications 3 Optimization Methods & Software 2 Journal of Computational Physics 2 Automatica 2 Journal of Computational and Applied Mathematics 2 Mathematical Programming. Series A. Series B 2 SIAM Journal on Optimization 2 Journal of Industrial and Management Optimization 1 Computers and Fluids 1 International Journal of Control 1 International Journal for Numerical Methods in Engineering 1 Optimal Control Applications & Methods 1 Operations Research Letters 1 Applied Numerical Mathematics 1 Finite Elements in Analysis and Design 1 Numerical Algorithms 1 Applied Mathematical Modelling 1 International Journal of Computer Mathematics 1 Advances in Engineering Software 1 ETNA. Electronic Transactions on Numerical Analysis 1 INFORMS Journal on Computing 1 Vietnam Journal of Mathematics 1 Multiscale Modeling & Simulation 1 Communications in Computational Physics 1 Discrete and Continuous Dynamical Systems. Series S 1 Algorithms 1 International Journal for Numerical Methods in Biomedical Engineering 1 SIAM Spotlights all top 5 Cited in 14 Fields 60 Numerical analysis (65-XX) 48 Operations research, mathematical programming (90-XX) 15 Calculus of variations and optimal control; optimization (49-XX) 7 Mechanics of deformable solids (74-XX) 6 Systems theory; control (93-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 3 Partial differential equations (35-XX) 3 Computer science (68-XX) 3 Fluid mechanics (76-XX) 2 Combinatorics (05-XX) 1 Ordinary differential equations (34-XX) 1 Integral equations (45-XX) 1 Statistics (62-XX) 1 Biology and other natural sciences (92-XX) Citations by Year