QMRPACK: A package of QMR algorithms. The quasi-minimal residual (QMR) algorithm is a Krylov-subspace method for the iterative solution of large non-Hermitian linear systems. QMR is based on the look-ahead Lanczos algorithm that, by itself, can also be used to obtain approximate eigenvalues of large non-Hermitian matrices. QMRPACK is a software package with Fortran 77 implementations of the QMR algorithm and variants thereof, and of the three-term and coupled two-term look-ahead Lanczos algorithms. In this article, we discuss some of the features of the algorithms in the package, with emphasis on the issues related to using the codes. We describe in some detail two routines from the package, one for the solution of linear systems and the other for the computation of eigenvalue approximations. We present some numerical examples from applications where QMRPACK was used.

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  1. Güttel, Stefan; Tisseur, Françoise: The nonlinear eigenvalue problem (2017)
  2. Bellavia, Stefania; De Simone, Valentina; di Serafino, Daniela; Morini, Benedetta: On the update of constraint preconditioners for regularized KKT systems (2016)
  3. Duintjer Tebbens, Jurjen; Meurant, Gérard: On the convergence of Q-OR and Q-MR Krylov methods for solving nonsymmetric linear systems (2016)
  4. Zimmerling, Jörn; Wei, Lei; Urbach, Paul; Remis, Rob: A Lanczos model-order reduction technique to efficiently simulate electromagnetic wave propagation in dispersive media (2016)
  5. Bellavia, Stefania; De Simone, Valentina; di Serafino, Daniela; Morini, Benedetta: Updating constraint preconditioners for KKT systems in quadratic programming via low-rank corrections (2015)
  6. Gu, Xian-Ming; Clemens, Markus; Huang, Ting-Zhu; Li, Liang: The CBiCG class of algorithms for complex symmetric linear systems with applications in several electromagnetic model problems (2015)
  7. Pestana, J.; Wathen, A. J.: A preconditioned MINRES method for nonsymmetric Toeplitz matrices (2015)
  8. Szyld, Daniel B.; Vecharynski, Eugene; Xue, Fei: Preconditioned eigensolvers for large-scale nonlinear Hermitian eigenproblems with variational characterizations. II. Interior eigenvalues (2015)
  9. Pestana, J.; Wathen, A. J.: Combination preconditioning of saddle point systems for positive definiteness. (2013)
  10. Agoujil, S.; Bentbib, A. H.; Kanber, A.: A structure preserving approximation method for Hamiltonian exponential matrices (2012)
  11. Sogabe, Tomohiro; Hoshi, Takeo; Zhang, Shao-Liang; Fujiwara, Takeo: Solution of generalized shifted linear systems with complex symmetric matrices (2012)
  12. Barbella, G.; Perotti, F.; Simoncini, V.: Block Krylov subspace methods for the computation of structural response to turbulent wind (2011)
  13. Bergamaschi, Luca; Gondzio, Jacek; Venturin, Manolo; Zilli, Giovanni: Erratum to: Inexact constraint preconditioners for linear systems arising in interior point methods (2011)
  14. D’Apuzzo, Marco; De Simone, Valentina; di Serafino, Daniela: On mutual impact of numerical linear algebra and large-scale optimization with focus on interior point methods (2010)
  15. Gupta, Anshul; George, Thomas: Adaptive techniques for improving the performance of incomplete factorization preconditioning (2010)
  16. Bellavia, Stefania; Gondzio, Jacek; Morini, Benedetta: Regularization and preconditioning of KKT systems arising in nonnegative least-squares problems (2009)
  17. Benzi, Michele; Haber, Eldad; Taralli, Lauren: Multilevel algorithms for large-scale interior point methods (2009)
  18. Bollhöfer, Matthias; Grote, Marcus J.; Schenk, Olaf: Algebraic multilevel preconditioner for the Helmholtz equation in heterogeneous media (2009)
  19. Hochstenbach, Michiel E.; Notay, Yvan: Controlling inner iterations in the Jacobi-Davidson method (2009)
  20. Bergamaschi, Luca; Ferronato, Massimiliano; Gambolati, Giuseppe: Mixed constraint preconditioners for the iterative solution of FE coupled consolidation equations (2008)

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