MINRES-QLP is created and developed by Sou-Cheng Choi (University of Chicago and Argonne National Laboratory), Christopher Paige (McGill University), and Michael Saunders (Stanford University). The MINRES-QLP Matlab/Octave package and MINRES-QLP Fortran 90 package are written and maintained by Sou-Cheng Choi and Michael Saunders.
-
MINRES-QLP PetSc implementation: Coming soon
-
MINRES-QLP Fortran 90/95 Package (Download from author's website or Download 937.zip from ACM, Bibtex)
-
MINRES in Matlab/Octave and Fortran 95
-
MINRES and MINRES-QLP Python with Theano and Numpy by Razvan Pascanu (Download)
-
ALGORITHM 937: MINRES-QLP for Symmetric and Hermitian Linear Equations and Least-Squares Problems. ACM Transactions on Mathematical Software, Volume 40, Number 2, 2014. (Offprint, Bibtex)
-
-
Minimal Residual Methods for Complex Symmetric, Skew Symmetric, and Skew Hermitian Systems. Report ANL/MCS-P3028-0812, Computation Institute, University of Chicago, 2013. (PDF, Bibtex)
-
ALGORITHM & DOCUMENTATION: MINRES-QLP for Symmetric and Hermitian Linear Equations and Least-Squares Problems. Report ANL/MCS-P3027-0812, Computation Institute, University of Chicago, 2012. (Report, Bibtex)
-
MINRES-QLP: A Krylov Subspace Method for Indefinite or Singular Symmetric Systems. SIAM Journal of Scientific Computing, Volume 33, Number 4, 1810-1836, 2011. (Offprint, Bibtex)
-
Iterative Methods for Singular Linear Equations and Least-Squares Problems. Ph.D. Dissertation, Stanford University, 2006. (bibtex)
-
Krylov and Saunders Subspace Methods, The Eleventh International Conference on Matrix Theory and Applications, Linyi University, Shangdong, People's Republic of China, June 15, 2014.
-
MINRES-QLP: a Krylov Subspace Method for Indefinite or Singular Symmetric Systems, SIAG/LA Prize Ceremony, SIAM Conference on Applied Linear Algebra, Universitat Politècnica de València, Valencia, Spain, June 21, 2012.
-
Krylov and Saunders Subspace Methods, Chinese Academy of Sciences, Beijing, People's Republic of China, June 20, 2014.
-
Reliable Reproducible Research in Computational Sciences through Sustainable Software Practices, Chinese Academy of Sciences, Beijing, People's Republic of China, June 19, 2014.
-
Generalized Minimal Residual Methods for Singular Linear Systems or Linear Least-Squares Problems, Applied Mathematics Colloquium, University of Maryland, Baltimore, Maryland, USA, May 9, 2014.
-
Minimal Residual Methods for Solving Singular Unsymmetric or Non-Hermitian Linear Equations, International Conference on Engineering and Computational Mathematics (ECM), Hong Kong, December 18, 2013.
-
Minimal Residual Methods for Solving Singular Unsymmetric or Non-Hermitian Linear Equations, Winter School for Scientific Computing, Taida Institute for Mathematical Sciences (TIMS), National Taiwan University, Taipei, Taiwan, December 5, 2013.
-
Minimal Residual Methods for Singular Hermitian, Complex Symmetric, or Skew Hermitian Linear Equations, Winter School for Scientific Computing, Taida Institute for Mathematical Sciences (TIMS), National Taiwan University, Taipei, Taiwan, December 5, 2013.
-
Krylov Solvers for Singular Hermitian, Complex Symmetric, or Skew Hermitian Linear Systems, The Center of Linear and Combinatorial Structures, University of Lisbon, Portugal, July 22, 2013.
-
MEGA-MINRES-QLP: A Krylov Solver for Singular Hermitian, Complex Symmetric, or Skew Hermitian Linear Systems or Least-Squares Problems, Young Mathematician Forum, Peking University, Beijing, People's Republic of China, June 18, 2013.
-
A Krylov Solver for Singular Hermitian, Complex Symmetric, or Skew Hermitian Linear Systems or Least-Squares Problems, School of Mathematical Sciences Seminars, Peking University, Beijing, People's Republic of China, June 16, 2013.
-
Minimal Residual Methods for Singular Complex Symmetric, Skew Symmetric, and Skew Hermitian Linear Systems and Least-Squares Problems, New Frontiers in Numerical Analysis and Scientific Computing: A conference on the occasion of Lothar Reichel's 60th birthday and on the 20th anniversary of ETNA, Kent, OH, April 19, 2013.
-
Extending MINRES and MINRES-QLP for Singular Linear Systems or Linear Least-Squares Problems with Special Symmetries, CCAM Lunch Seminar, Purdue University, West Lafayette, IN, April 5, 2013.
-
Minimal Residual Methods for Singular Complex Symmetric, Skew Symmetric, or Skew Hermitian Linear Systems, Algorithms Seminar, Duke University, Durham, NC, March 11, 2013.
-
Krylov Solvers for Singular Symmetric, Hermitian, Complex Symmetric, or Skew Symmetric Linear Systems, CSC Seminar, Simon Fraser University, BC, Canada, November 2, 2012.
-
Krylov Solvers for Singular Symmetric, Hermitian, Complex Symmetric, or Skew Symmetric Linear Systems, Structured Linear Algebra Problems: Analysis, Algorithms and Applications, KU Leuven, Leuven, Belgium, September 10, 2012.
-
Krylov Subspace Methods for Solving Singular Linear Systems or Least-Squares Problems, SIAM Annual Meeting, Chicago, IL, July 8, 2014.
-
Extending GMRES for Singular Systems of Equations, Mid-West Numerical Analysis Day, Milwaukee, Wisconsin, May 3, 2014.
-
Generalized Minimal Residual Methods for Singular Linear Systems or Linear Least-Squares Problems, Copper Mountain Conference on Iterative Methods, Denver, Colorado, April 7, 2014.
-
Krylov Solvers for Singular Hermitian, Complex Symmetric, or Skew Hermitian Linear Systems, SIAM Conference on Computational Science and Engineering, Boston, MA, February 25, 2013.
-
MINRES-QLP: A Krylov Subspace Method for Singular Symmetric Linear Equations and Least-Squares Problems, Stanford 50: State of the Art and Future Directions of Computational Mathematics and Numerical Computing, Stanford, CA, March 29, 2007.
-
Good Practices for Mathematical Software, Meshfree Methods Seminar, Department of Applied Mathematics, Illinois Institute of Technology, Chicago IL, May 21, 2014.
-
Matrix Computations and Data Sciences, NORC at the University of Chicago, Chicago, IL, January 15, 2014.
-
A MINRES-QLP-Like Algorithm for Solving Complex Symmetric Linear Systems and Least-Squares Problems, Meshfree Methods Seminar, Illinois Institute of Technology, Chicago, IL, May 29, 2012.
-
MINRES-QLP for Singular Symmetric and Hermitian Linear Equations and Least-Squares Problems, LANS Informal Seminar, Argonne National Laboratory, Argonne, IL, December 14, 2011.
-
MINRES-QLP and its Application to Radial Basis Function Interpolation, Meshfree Methods Seminar, Illinois Institute of Technology, Chicago IL, April 11, 2011.
-
MINRES-QLP: A Krylov Subspace Method for Singular Symmetric Linear Equations and Least-Squares Problems, Institute for Computational Mathematics, Hong Kong Baptist University, Hong Kong, January 15, 2009.
-
MINRES-QLP: A Krylov Subspace Method for Singular Symmetric Linear Equations and Least-Squares Problems, UC Berkeley linear algebra (LAPACK) seminar, Berkeley, CA, January 17, 2007.
-
Auto-Regressive Moving Average Models on Complex-Valued Matrix Lie Groups. Circuits, Systems, and Signal Processing (2014): 1-25.
-
Discrete Hodge Theory on Graphs: A Tutorial. Computing in Science and Engineering 15.5 (2013): 42-55.
-
Computational Precision of Traffic Equilibria Sensitivities in Automatic Network Design and Road Pricing. Procedia-Social and Behavioral Sciences 80 (2013): 41-60.
-
Rank Awareness in Group-Sparse Recovery of Multi-Echo MR Images. Sensors 13.3 (2013): 3902-3921.
-
Do You Trust Derivatives or Differences? Report ANL/MCS-P2067-0312, Mathematics and Computer Science Division, Argonne National Laboratory (2012).
-
Simultaneous Analysis and Design in PDE-Constrained Optimization. Ph.D. Dissertation, Stanford University, 2012.
-
Improved dynamic MRI reconstruction by exploiting sparsity and rank-deficiency. Magnetic Resonance Imaging (2012).
-
Computation and modeling for high dimensional Gaussian distributions. Diss. Norwegian University of Science and Technology, 2012.
-
CG Versus MINRES: An Empirical Comparison. SQU Journal for Science 17.1 (2012): 44-62.
-
Stability of space-time Petrov-Galerkin discretizations for parabolic evolution equations. Diss. Diss., Eidgenössische Technische Hochschule ETH Zürich, Nr. 20842, 2012.
-
LSMR: An iterative algorithm for sparse least-squares problems. SIAM Journal on Scientific Computing 33.5 (2011): 2950-2971.
-
Statistical ranking and combinatorial Hodge theory. Mathematical Programming, Special Issue on Optimization and Machine Learning, 127 (2011), no. 1, pp. 203–244.
-
Fast sparse Cholesky decomposition and inversion using nested dissection matrix reordering. Journal of Chemical Theory and Computation 7.2 (2011): 351-368.
-
Acquired clustering properties and solution of certain saddle point systems. SIAM Journal on Matrix Analysis and Applications 31.5 (2010): 2754-2768.
-
Convergence properties of the primal and dual forms of variational data assimilation. Quarterly Journal of the Royal Meteorological Society 136.646 (2010): 107-115.
-
Stopping criteria for the iterative solution of linear least squares problems. SIAM Journal on Matrix Analysis and Applications 31.2 (2009): 831-852.
-
A matrix-free algorithm for equality constrained optimization problems with rank-deficient Jacobians. SIAM Journal on Optimization 20.3 (2009): 1224-1249.
-
Methods for the physically based simulation of solids and fluids. Diss. Stanford University, 2007.
Our work was supported in part by grants from
-
the Office of Advanced Scientifi c Computing Research, Office of Science, U.S. Department of Energy, under contract DE-AC02-06CH11357
-
the National Science Foundation grant CCR-0306662
-
the Office of Naval Research grants N00014-02-1-0076 and N00014-08-1-0191; and U.S. Army Research Laboratory through the Army High Performance Computing Research Center.
-
Charter Renewal Application For The Siam Activity Group On Linear Algebra
-
Professor Michael Saunders of MS&E is a co-winner of the 2012 SIAG/LA Prize
-
Professor Saunders along with Christopher Paige and Sou-Cheng Choi earn the SIAG/Linear algebra Prize for their paper, "MINRES-QLP: A Kryloz Subspace Method for Indefinite or Singular Symmetric Systems" (Photo)
- Refer to our Wiki pages for information and frequently asked questions.
- Review and search Issues for your questions about MINRES-QLP. If it does not help, you may file a new issue ticket and we will respond as soon as we could.
- Email questions and comments to [email protected].
If you would like to contribute to the software development or documentation of the framework, please contact [email protected].