• J. Scott and M. Tuma. Developing robust incomplete Cholesky factorizations in half precision arithmetic Numerical Algorithms, 2025, to appear. [pdf ]
• J. Scott and M. Tuma. Avoiding breakdown in incomplete factorizations in low precision arithmetic (2024, ACM Transactions of Mathematical Software, to appear). [pdf (currently from arXiv) ]
• J. Scott and M. Tuma. Algorithms for Sparse Linear Systems Birkhauser 2023, open access. [pdf]
• J. Scott and M. Tuma. Solving large linear least squares problems with linear equality constraints BIT 62 (2022), no. 4, 1765–1787. [pdf]
• J. Scott and M. Tuma. A null-space approach for symmetric saddle point systems with a small (2,2) block Numerical Algorithms, 90 (2022), no. 4, 1639–1667. [pdf]
• J. Scott and M. Tuma. A computational study of using black-box QR solvers for large-scale sparse-dense linear least squares problems ACM Transactions on Numerical Software, 48(1), 5, 2022, 25 pages. [pdf]
• J. Scott and M. Tuma. Strengths and limitations of stretching for least-squares problems with some dense rows ACM Transactions on Numerical Software, 47(1), 1, 2020, 25 pages. [pdf]
• J. Scott and M. Tuma. Sparse stretching for solving sparse-dense linear least squares problems, SIAM J. Sci. Comput. 41 (2019), A1604-A1625. [pdf]
• E.C. Carson, M. Rozloznik, Z. Strakos, P. Tichy and M. Tuma. On the numerical stability analysis of pipelined Krylov subspace methods, SIAM J. Sci. Comput. 40 (2018), A3549-A3580. [pdf]
• J. Scott and M. Tuma. A Schur complement approach to preconditioning sparse linear least-squares problems with some dense rows Numerical Algorithms, 79 (2018), 1147-1168.
  https://doi.org/10.1007/s11075-018-0478-2 [pdf]
• R. Cimrman, M. Novak, R. Kolman, M. Tuma and J. Vackar. Isogeometric analysis in electronic structure calculations, Math. Comput. Simulation 145 (2018), 125-135.
• R. Cimrman, M. Novak, R. Kolman, M. Tuma J. Plesek and J. Vackar. Convergence study of isogeometric analysis based on Bézier extraction in electronic structure calculations,
  Appl. Math. Comput. 319 (2018), 138-152.
• J. Scott and M. Tuma. Solving mixed sparse-dense linear least squares by preconditioned iterative methods SIAM J Sci. Comput., 39(2017), A2422-A2437. [pdf]
• J. Scott and M. Tuma. Improving the stability and robustness of incomplete symmetric indefinite factorization preconditioners, Numerical Linear Algebra with Applications, 24(2017), No. 5, e2099, 18pp. [pdf]
• J. Kopal, M. Rozloznik and M. Tuma. An adaptive multilevel factorized sparse approximate inverse preconditioning, Advances in Engineering Software, 113 (2017), 19-24. [pdf]
• J. Scott and M. Tuma. Preconditioning of linear least squares by RIF for implicitly held normal equations SIAM J Sci. Comput., 38(2016), C603--C623. [pdf]
• J. Kopal, M. Rozloznik and M. Tuma. Factorized approximate inverses with adaptive dropping, SIAM J. Sci. Comput., 38 (3),2016, A1807-A1820. [pdf]
• J. Kopal, M. Rozloznik and M. Tuma. Approximate inverse preconditioners with adaptive dropping, Advances in Engineering Software, 84 (2015), 13-20.
• J. Scott and M. Tuma. On signed incomplete Cholesky factorization preconditioners for saddle-point systems, SIAM J Sci. Comput., 36(2014), A2984--A3010. [pdf]
• R. Bru, J. Marin, J. Mas and M. Tuma. Preconditioned iterative methods for solving linear least squares problems , SIAM J Sci. Comput., 36(2014), A2002--A2022. [pdf]
• J. Scott and M. Tuma. On positive semidefinite modification schemes for incomplete Cholesky factorization, SIAM J. Sci. Comput., 36 (2014), pp. A609--A633. [pdf]
• J. Duintjer Tebbens and M. Tuma. On incremental condition estimators in the 2-norm , SIAM J. Matrix Anal. Appl. 35 (2014), 174--197. [pdf]
• J. Scott and M. Tuma. HSL_MI28: an efficient and robust limited memory incomplete Cholesky factorization code, ACM Trans. Math. Software, 40 (2014), article 24, 1--19. [pdf]
• R. Kouhia, M. Tuma, J. Makinen, A. Fedoroff and H. Marjamaki. Implementation of a direct procedure for critical point computations using preconditioned iterative solver,
  Computers and Structures, 108-109 (2012), 110-117.
• J. Kopal, M. Rozloznik, A. Smoktunowicz and M. Tuma. Rounding error analysis of orthogonalization with a non-standard inner product, BIT Numer Math 52(2012), pp. 1035-1058. [pdf]
• J. Scott and M. Tuma. The importance of structure in algebraic preconditioners, BIT Numer Math, 51(2011), pp. 385-404. [pdf]
• R. Bru, J. Marin, J. Mas and M. Tuma. Improved balanced incomplete factorization , SIAM J Matrix Anal Appl, 31(2010), pp. 2431-2452. [pdf]
• J. Duintjer Tebbens and M. Tuma. Preconditioner updates for solving sequences of linear systems in matrix-free environment, Numerical Linear Algebra with Applications, 17(2010), 997-1019. [pdf]
• R. Bru, J. Marin, J. Mas and M. Tuma. Balanced incomplete factorization, SIAM Journal on Scientific Computing, 30 (2008), 2302-2318. [pdf]
• P. Birken, J. Duintjer Tebbens and Andreas Meister and M. Tuma. Preconditioner updates applied to CFD model problems , Applied Numerical Mathematics, 58(2008), 1628-1641. [pdf]
• J. Duintjer Tebbens and M. Tuma. Preconditioner updates for solving sequences of large and sparse nonsymmetric linear systems , SIAM Journal on Scientific Computing, 29 (2007), 1918-1941. [pdf]
• J. Cullum and M. Tuma. Matrix-Free Preconditioning Using Partial Matrix Estimation , BIT, 46(2006), 711-729. [pdf]
• M.Arioli , J. Maryska, M. Rozloznik, and M. Tuma. Dual variable methods for mixed-hybrid finite element approximation of the potential fluid flow problem in porous media, , ETNA, 22 (2006), 17-40. [pdf]
• M. Benzi and M. Tuma. A Robust Preconditioner with Low Memory Requirements for for Large Sparse Least Squares Problems, SIAM Journal on Scientific Computing, 25 (2003), pp. 499-512. [gzipped ps]
• M. Benzi and M. Tuma. A Robust Incomplete Factorization Preconditioner for Positive Definite Matrices, Numerical Linear Algebra with Applications, 10 (2003), pp. 385-400. [gzipped ps]
• J.K. Cullum and K. Johnson and M. Tuma. Effects of problem decomposition on the convergence behavior of parallel numerical algorithms , Numerical Linear Algebra with Applications, 10 (2003), pp. 445-465. [pdf]
• M. Tuma, A note on the $LDL^T$ decomposition of matrices from saddle-point problems, SIAM J. Matrix Anal. Appl. 23(2002), 903 - 915. [ps]
• M. Benzi and M. Tuma. A Parallel Solver for Large-Scale Markov Chains, Applied Num. Math. 41(2002), 135 - 153. [gzipped ps]
• M. Benzi and R. Kouhia and M. Tuma. Stabilized and Block Approximate Inverse Preconditioners for Problems in Solid and Structural Mechanics, Computer Methods in Applied Mechanics and Engineering, 190 (2001), pp. 6533-6554. [ps file]
• M. Benzi and J.C. Haws and M. Tuma. Preconditioning Highly Indefinite and Nonsymmetric Matrices, SIAM J. Sci. Comput. 21 (2000), 1333--1353.
• M. Benzi and J.K. Cullum and M. Tuma. Robust Approximate Inverse Preconditioning for the Conjugate Gradient Method, SIAM J. Sci. Comput. 22 (2000), 1318--1332.
• M. Benzi and M. Tuma. Orderings for factorized sparse approximate inverse preconditioners, SIAM J. Sci. Comput. 21 (2000), 1851--1868.
• J. Maryska, M. Rozloznik, M. Tuma, Schur complement systems in the mixed-hybrid finite element approximation of the potential fluid flow problem, SIAM J. Sci. Comput. 22 (2000), 704--723.
• J. Maryska, M. Rozloznik, M. Tuma, Solution of augmented systems from a mixed-hybrid finite element discretization of the potential fluid flow problem: Asymptotic rates of convergence, Proceedings of Algoritmy 2000, 100--109 [ps].
• J. Maryska, M. Rozloznik, M. Tuma, Schur complement reduction in the mixed-hybrid approximation of the Darcy's law: Rounding error analysis, J. Comput. Appl. Math. 117 (2000), 159--173 ,
• M. Benzi , J. Marin, M. Tuma. A Two-Level Parallel Preconditioner Based on Sparse Approximate Inverses, in: Iterative Methods in Scientific Computation IV, D. R. Kincaid and A. C. Elster, eds., IMACS Series in Computational and Applied Mathematics, Vol. 5, IMACS, New Brunswick, NJ (1999), pp. 167-178.
• M. Benzi and M. Tuma. A Comparative Study of Sparse Approximate Inverse Preconditioners , LA-UR-98-0024, January 1998, Applied Numerical Mathematics 30 (1999), 305--340.
• M. Benzi , R. Kouhia and M. Tuma. An Assessment of Some Preconditioning Techniques in Shell Problems , Communications in Numerical Methods in Engineering 14 (1998), pp. 897-906.
• M. Benzi and M. Tuma, Numerical Experiments with Two Approximate Inverse Preconditioners, BIT , vol.38, 1998, pp. 234--241.
• M. Benzi and M. Tuma, A sparse approximate inverse preconditioner for nonsymmetric linear systems, SIAM J. Sci. Comput., 19 (1998), pp. 968--994.
• M. Benzi , C.D. Meyer and M. Tuma, A sparse approximate inverse preconditioner for the conjugate gradient method, Stat. J. Sci. Comput., 17(1996), pp. 1135--1149.
• M. Benzi and M. Tuma, A comparison of some preconditioning techniques for general sparse matrices, in: Iterative Methods in Linear Algebra, II, S.D. Margenov, P.S. Vassilevski, eds., IMACS Series in Computational and Applied Mathematics, Vol. 3, IMACS, (1996), pp. 191--203.
• M. Benzi and M. Tuma, Approximate inverse preconditioning for the conjugate gradient method on a vector computer, in: Proceedings of the Prague Mathematical Conference 1996 (K. Segeth Ed.), Prague, 29-34, 1996, [ps].
• M. Rozloznik, Z. Strakos, M. Tuma, On the Role of Orthogonality in the GMRES Method, in SOFSEM'96: Theory and Practice of Informatics, K. Jeffery, J. Kral, M. Bartosek (Eds.), Lecture Notes In Computer Science, Vol. 1175, Springer Verlag, (1996), pp. 409-416, [ps], [dvi].
• J. Maryska, M. Rozloznik, M. Tuma, The potential fluid flow problem and the convergence rate of the minimal residual method, Numerical Linear Algebra with Applications, Vol. 3(6), (1996), pp. 525-542, (also Research report 634, ICS AS CR, Prague, (1995), pp. 17), [ps], [dvi].
• M. Benzi and M. Tuma, Preconditioning with sparse approximate inverses, in: Proceedings of the XI. Summer School Numerical Algorithms and Software, I. Marek et al. (eds.), University of West Bohemia, (1996), pp. 5-16.
• M. Benzi and M. Tuma, Approximate inverse preconditioning of iterative methods for nonsymmetric linear systems, in: Proceedings of Copper Mountain Conference on Iterative Methods, Copper Mountain, Colorado, 1-6, 1996.
• M. Tuma, M. Rozloznik, On the efficiency of superscalar and vector computers for some problems in scientific computing, in SOFSEM'95: Theory and Practice of Informatics, M. Bartosek, J. Staudek, J. Wiedermann (Eds.), Lecture Notes In Computer Science, Vol. 1012, Springer Verlag, (1995), pp. 481-486, [ps], [dvi].
• J. Maryska , M. Rozloznik, M. Tuma, Mixed-hybrid finite element approximation of the potential fluid flow problem, J. Comp. Appl. Math. 63 (1995), pp. 383-392, [ps], [dvi].
• Z. Strakos, M. Tuma, Current Trends in Numerical Linear Algebra: From Theory to Practice, Proceedings of the SOFSEM'94, M. Bartosek (ed.), Brno, Czech Soc. of Comp. Science, (1994), pp. 229-249, [pdf] .
• M. Tuma, Implicit Gauss Algorithm for Solving the Sparse Unsymmetric Sets of Linear Equations, Technical Report CSGS 1/85, University of Bergamo, (1992).

Other publications

• P. Birken, J. Duintjer Tebbens, Andreas Meister and M. Tuma. Improving Triangular Preconditioner Updates for Nonsymmetric Linear Systems , Proc. Appl. Math. Mech. 7, 1022101-1022102 (electronic), 2007
• P. Birken, J. Duintjer Tebbens, Andreas Meister and M. Tuma. Updating Preconditioners for Permuted Nonsymmetric Linear Systems , Lecture Notes in Computer Science 4818 (2008), 737-744.
• M. Rozloznik, Z. Strakos, M. Tuma, Do We Really Need Well Preserved Orthogonality in the GMRES method ?, In: 5-th. Conference of the International Linear Algebra Society, Chemnitz, Germany, 1996 (abstract).
• M. Tuma A Quadratic Programming Algorithm for Large and Sparse Problems., Cybernetics 27(1991), pp. 155-167.
• M. Tuma Sparse Fractioned Variable Metric Updates, Research Report No. 497, ICIS CSAV, Prague, (1991).
• M. Tuma Parallel algorithms in optimization, in: The Proceedings of the conference Algorithms '91, Vysoke Tatry, CSFR, (1991).
• M. Tuma Large and Sparse Quadratic Programming, Ph.D. Thesis, UIVT CSAV, Prague, (1989).
• M. Tuma A Note on Direct Methods for Approximations of Sparse Hessian Matrices, Applications of Mathematics, 33(1988), pp. 171-176.
• L. Luksan, M. Tuma UFO - subprograms for the operations with the symmetric matrices, Research Report V - 309, Prague, SVT CSAV, (1987).
• J. Reiterman, V. Rodl, E. Sinajova and M. Tuma Threshold Hypergraphs, Discrete Mathematics 54(1985), pp. 193-200.
• J. Reiterman, V. Rodl, E. Sinajova, M. Tuma Note on Threshold Hypergraphs, Acta Polytechnica, (1982), pp. 39-46.

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