Recent Research
Reports:
Journal publications:
- M. Rozloznik,
G. Shklarski
and S.
Toledo: Partitioned triangular tridiagonalization, ACM Transactions
on Mathematical Software (TOMS) 37(4):38 (2011).
- P. Jiranek,
M. Rozloznik: Adaptive version of Simpler GMRES. Num. Algorithms Volume 53, Issue
1 (2010), Page 93
- P. Jiranek,
M. Rozloznik, M.H. Gutknecht:
How
to make simpler GMRES and GCR more stable,
SIAM Journal of Matrix Analysis and Applications (2008), Vol. 30, No. 4, pp. 1483-1499.
- P. Jiranek,
M. Rozloznik: Maximum attainable
accuracy of inexact saddle point solvers, SIAM Journal of Matrix Analysis and Applications (2008),
Vol. 29, No. 4, pp. 1297—1321.
- P. Jiranek,
M. Rozloznik: Limiting
accuracy of segregated solution methods for nonsymmetric saddle point problems, Journal of Computational and Applied Mathematics 215
(2008), pp. 28-37.
- C.C. Paige,
M. Rozloznik, Z. Strakos:
Modified
Gram-Schmidt (MGS), least squares
and backward
stability of
MGS-GMRES, SIAM J. Matrix Anal. and Appl. (2006), Vol. 28, No. 1, pp.
264--284.
- M. Arioli, J. Maryska, M. Rozloznik,M. Tuma: Dual
variable methods for mixed-hzbrid finite element approximation
of the potential fluid flow problem in porous media, ETNA (2006), Vol. 22, pp. 17-40.
- L. Giraud,
J. Langou, M. Rozlozník,
and J. van den Eshof : Rounding error analysis of the classical Gram-Schmidt orthogonalization process
, Numerische Mathematik
(2005) 101: 87-100 (previous version
without the result on CGS: L. Giraud, J.
Langou , M. Rozloznik: On the round-off error analysis of the Gram-Schmidt algorithm with reorthogonalization,
Research Report TR/PA/02/33, CERFACS, Toulouse,
France, April, 2002).
- L. Giraud,
J. Langou,
M. Rozloznik: On the
loss of orthogonality in the
Gram-Schmidt orthogonalization process ,
Computers & Mathematics
with Applications 50
(2005), pp. 1069--1075.
- M. Rozloznik,
V. Simoncini : Krylov
subspace methods for saddle point problems with indefinite preconditioning , SIAM J. Matrix Anal. and Appl. (2002), Vol. 24,
No. 2, pp. 368--391.
- J. Liesen, M. Rozloznik,
Z. Strakos : Least squares residuals and minimal residual methods , SIAM J. Sci. Comput. (2002), Vol. 23, No. 5, pp.
1503-1525 .
- M. H. Gutknecht
, M. Rozloznik: A framework for generalized conjugate gradient methods -
with special emphasis on contributions
by Ruediger Weiss, Applied
Numerical Mathematics
(APNUM) 41 (2002), 7-22.
- M.H. Gutknecht,
M. Rozloznik: Residual smoothing techniques: Do they improve the limiting accuracy of iterative solvers? , BIT 41, No. 1 (2001), 86--114.
- M. H. Gutknecht
, M. Rozloznik: By how
much can residual
minimization accelerate
the convergence of orthogonal residual methods?
, Numerical Algorithms
27 (2001), 189-213.
- J. Maryska,
M. Rozloznik, M. Tuma
: Schur
complement systems in the mixed-hybrid finite element of the potential fluid flow problem
, SIAM J. Sci. Comput.
(SISC), Vol 22, No. 2 (2000), 704-723.
- J. Maryska
, M. Rozloznik, M. Tuma
: Schur
complement reduction
in the mixed-hybrid approximation of Darcy's law: Rounding error analysis , J. Comp. Appl. Math. 117 (2000), 159-173.
- M. Rozloznik,
R. Weiss: On the
stable implementation of the Generalized
minimal error method , J. Comp.
Appl. Math. 98 (1998),
pp. 49-62.
- A. Greenbaum
, M. Rozloznik, Z. Strakos
: Numerical
behaviour of the modified Gram-Schmidt
GMRES implementation , BIT 37:3
(1997), pp. 706-719.
- 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.
- J. Drkosova,
A. Greenbaum, M. Rozloznik,
Z. Strakos : Numerical
stability of GMRES, BIT 35:3 (1995), pp. 309-330.
- 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.
Conference Publications:
- M. Rozloznik:
Saddle point problems, iterative solution and preconditioning: a short overview, Proceedings of the XV-th Summer School Software and Algorithms of Numerical Mathematics, I.
Marek ed., University of
West Bohemia, Pilsen,
(2003).
- J. Maryska,
M. Rozloznik, M.Tuma: Primal
vs. dual variable
approach for mixed-hybrid
finite element approximation
of the potential fluid flow problem in porous media,
Proceedings of the 3rd International Conference on "Large-Scale Scientific Computations", Lecture
Notes in Computer Science 2179, Sv. Margenov, J. Wasniewski, P. Yalamov (eds.), June 6-10,
2001, pp.417-424.
- 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), K. Mikula et al (eds), Vysoke Tatry, Slovakia,
pp. 100-109.
- 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,
Berlin, Heidelberg, (1996), pp. 409-416.
- M. Rozloznik,
Z. Strakos : Variants
of the residual minimizing Krylov space methods, in Proceedings
of the XI-th Summer School Software and Algorithms of Numerical Mathematics, I.
Marek ed., University of
West Bohemia, Pilsen,
(1995), pp. 208-225.
- M. Rozloznik,
Z. Strakos : On the
implementation of some residual minimizing Krylov space methods,
in SOFSEM'95: Theory and
Practice of Informatics, M. Bartosek ,
J. Staudek, J. Wiedermann (Eds),
Lecture Notes in Computer
Science, Vol. 1012, Springer Verlag,
Berlin, Heidelberg, (1995), pp. 449-454.
- 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,
Berlin, Heidelberg, (1995), pp. 481-486.
- M. Kocvara
, M. Rozloznik, S.L.Xanthis:
On
iterative solvers for the method of arbitrary lines, in E.A. Lipitakis,
Proceedings of the Second Hellenic European Conference on Mathematics and Informatics - HERMIS'94,
Hellenic Mathematical
Society, Athens, Greece,
(1995), pp. 261-272.
PhD-Thesis: M. Rozloznik:
Numerical Stability of the GMRES Method , PhD Thesis, Institute of Computer Science, Academy of Sciences of
the Czech Republic and Faculty
of Nuclear Science and Physical Engineering,
Czech Technical University,
Prague (1997), p.80 (available
on the request in the printed form
from the author)
Habilitation Thesis: M. Rozloznik: Iterative solution of saddle point problems in mathematical modelling (in Slovak),
Iterative solution of Technical University of Liberec, Department of Modelling of Processes,
Faculty of Mechatronics and Interdisciplinary Studies,
Liberec, April 2004. Shorter
version but in English available as: Saddle point problems, iterative solution and preconditioning: a short overview, submitted to Proceedings of the XV-th
Summer School Software and Algorithms of Numerical Mathematics,
I. Marek ed., University of
West Bohemia, Pilsen,
(2003).
Homepage of the Krylov
project
Miro Rozloznik--(miro@cs.cas.cz) --Last Revision December 2, 2011.