Katedra matematiky

Papers, Conferences etc., Lecture notes, Grants

Papers

2014-2020

M. Čertíková, L. Gaynudtinova, I. P., Multilevel a posteriori error estimator for greedy reduced basis algorithms. SN Applied Sciences. 2020. (Online ref.)
M. Ladecký, I. P., Jan Zeman, Guaranteed two-sided bounds on all eigenvalues of preconditioned iffusion and elasticity problems solved by the finite elements method. Submitted. (Arxiv-preprint)
M. Kubínová, I. P., Block Preconditioning of Stochastic Galerkin Problems: New Two-sided Guaranteed Spectral Bounds, SIAM/ASA Journal of Uncertainty Quantification. 2020, Vol. 8, No. 1, pp. 88-113. (Arxiv-preprint).
J. Hrnčíř, I. P., Z. Strakoš, Decomposition into subspaces preconditioning: abstract framework. Numerical Algorithms. 2020, 83(1), 57-98. ISSN 1017-1398.
M. Plešinger, I. P., On the extreme eigenvalues of certain matrices of non-standard inner products of Hermite polynomials Linear Algebra and Its Applications. 2018, 546, 50-66. ISSN 0024-3795. Ref.
I. P., Block and multilevel preconditioning for stochastic Galerkin problems with lognormally distributed parameters and tensor product polynomials International Journal for Uncertainty Quantification. 2017, 7(5), 441-462. ISSN 2152-5080. Ref.
I. P., P. Vaněk, Convergence theory for the exact interpolation scheme with approximation vector as the first column of the prolongator and Rayleigh quotient iteration nonlinear smoother Applications of mathematics. 2017, 62(1), p. 49-73. ISSN 0862-7940.
I. P., Hierarchical preconditioning for the stochastic Galerkin method: upper bounds to the strengthened CBS constants. Computers and Mathematics with Applications. 2016, vol. 71, no. 4, p. 949-964. ISSN 0898-1221. Ref.
I. P., Convergence theory of exact interpolation scheme for computing several eigenvectors. Numerical Linear Algebra with Applications. 2016, vol. 23, no. 2, p. 373-390. ISSN 1070-5325.
I. P., Adaptive algorithm for stochastic Galerkin method. Applications of Mathematics. 2015, vol. 60, no. 5, p. 551-571. ISSN 0862-7940. Ref.

2013

I. P., Fourier analysis of the aggregation based algebraic multigrid for stochastic matrices. SIAM Journal on Matrix Analysis and Applications. 2013, vol. 34, no. 4, p. 1596-1610. ISSN 0895-4798. 2012

I. P., Error propagation formula of multi-level iterative aggregation-disaggregation methods for non-symmetric problems. The Electronic Journal of Linear Algebra, 2012, vol. 25, pp. 9-21, ISSN 1081-3810. ref.
I. P., Fourier analysis of iterative aggregation- disaggregation methods for nearly circulant stochastic matrices. Proceedings of Seminar Programs and Algorithms of Numerical Mathematics 16. Praha: Academy of Sciences of the Czech Republic, 2013, p. 168-173. ISBN 978-80-85823-62-2.

2011

I. P., Preconditioning of the coarse problem in the method of balanced domain decomposition by constraints. Mathematics and Computers in Simulation. ref.
I. P., I. Marek, Convergence of multi-level iterative aggregation-disaggregation methods. Journal of Computational and Applied Mathematics, 2011, vol. 236, pp. 354-363, ISSN 0377-0427.
I. P., I. Marek, Physiology and pathology of iterative aggregation–disaggregation methods. Numerical Linear Algebra and Its Applications, 2011, vol. 18, pp. 1051-1065, ISSN 1070-5325.
I. P., Error estimates and domain decomposition methods. SNA'11 Seminar on Numerical Analysis. Modelling and Simulation of Challenging Engineering Problems, 2011, pp. 34-37, ISBN 978-80-86407-19-7.

2010

I. P., Coarse problems of balanced domain decomposition methods by constraints, Proceedings of Seminar on Numerical Analysis, Nove Hrady, 2010.
I. P., Unboundedness of spectral radii of asymptotic error propagation matrices of iterative aggregation - disaggregation methods, preprint.
I. Marek, P. Mayer, I. P., A study of convergence of multilevel iterative aggregation - disaggregation methods, Proceedings of NSMC conference, Williamsburg, 2010.

2009

I. P., Preconditioning and a posteriori error estimates using h- and p-hierarchical finite elements with rectangular supports. Numerical Linear Algebra with Applications 16, 2009, pp. 415-430, ISSN 1070-5325, ref.
I. Marek, P. Mayer, I. P., Convergence issues in the theory and practice of iterative aggregation/disaggregation methods. Electronic Transactions on Numerical Analysis (online). 2009, vol. 35, no. 35, p. 185-200, ISSN 1068-9613, ref.
I. P., Ordering of matrices for iterative aggregation - disaggregation methods. Lecture Notes in Control and Information Sciences. 2009, vol. 2009, no. 389, p. 379-386, ISSN 0170-8643.
I. P., Modifications of IAD methods for large scale computing. Seminar on Numerical Analysis, Modelling and Simulation of Challenging Engineering Problems. Ostrava: Ústav geoniky AV ČR, 2009, vol. 1, p. 41-42. ISBN 978-80-86407-60-9.
I. P., AML preconditioning of coarse problems in the BDDC method. Technical Computing Prague 2009, 2009, vol. 1, p. 86-89, ISBN 978-80-7080-733-0.

2008

I. P., Hierarchical bases on rectangles. Proceedings of the Seminar on Numerical Analysis (SNA), Liberec, January 2008.
I. P., Necessary and sufficient local convergence condition of one class of iterative aggregation- diasaggregation methods. Numerical Linear Algebra with Applications 15, 2008, pp. 339-354, ref.
I. P., Preconditioning and a posteriori error estimates using h- and p-hierarchical finite elements with rectangular supports. Submitted.

2007

I. P., Local convergence analysis of iterative aggregation–disaggregation methods with polynomial correction, Linear Algebra and its Applications 421, 2007, ref.
I. Marek, P. Mayer, I. P., Convergence of iterative aggregation/disaggregation methods based on splittings with cyclic iteration matrices, Dagstuhl Seminar Proceedings, 2007, ref .
I. P., A posteriori error estimates for hierarchical bases, Proceedings of Seminar on Numerical Analysis (SNA) 2007, Ostrava, January 2007.

2006

I. P., Heat conduction in radioactive waste repository, submitted to Proceedings of Technical Computing Prague, Praha, 2006.
I. P., Two partial results on preconditioning using hierarchical bilinear finite elements, submitted to the proceedings of SANM 2005, pdf
I. P., Convergence of some classes of IAD methods in computing Markov chains, Proceedings Seminar on Numerical Analysis (SNA) 2006, Moninec, January 2006
I. Marek, I. P., A note on local and global convergence analysis of iterative aggregation–disaggregation methods, Linear Algebra and its Applications 413, 2006, pp. 327-341, ref

2005

I. P., Strengthened C.B.S. Inequality Constant for Second Order Elliptic Partial Differential Operator and for Hierarchical Bilinear Finite Element Functions, Applications of Mathematics 50, 2005, pp. 323-329, ref.
I. P., Lokální a globální konvergence iterační agregační metody pro nalezení vektoru stacionárního rozdělení pravděpodobnosti stochastické matice, Sborník odborného semináře Funkční způsobilost a optimalizace stavebních konstrukcí, Fakulta stavební ČVUT, Praha, 2005
I. P., Google search engine - some computing experience, proceedings of Seminar on Numerical Analysis, Modelling and Simulation of Challenging Engineering Problems, Ostrava, 2005
I. P., Tarjan's algorithm in computing PageRank, Proceedings of Technical Computing Prague, Praha, 2005

2004

I. P., The strengthened C.B.S. inequality constant for hierarchical bilinear finite element functions, Proceedings of the conference Iterartive methods, preconditioning & numerical PDEs (IMET 2004), 2004
I. P., Multilevel Solution of Some Problems with Fast Changing Data, CTU Reports, Proceedings of Workshop 2004

2003

I. P., Multilevel bases for second order elliptic partial differential equations with variable coefficients, submitted to International Journal of Computational Engineering Science, 2003, pdf
I. P., Víceúrovňové baze a předpodmínění FSAI, sborník Konference MATLAB 2003, Praha
I. P., Multilevel bases and SAINV preconditioning for second order elliptic problems, sborník semináře Matematika na vysokých školách, Herbertov, 2003
I. P., Multilevel treatment of second order partial differential equations with variable coefficients, Proceedings of the Mathematical and Computer Modelling in Science and Engineering, 2003, Prague

2002

I. P., Časově-frekvenční analýza zvuku, Sborník odborného semináře "Funkční způsobilost a optimalizace staveb", ČVUT, Fakulta stavební, Praha 2002
I. P., O.Zindulka, Application of computing system matlab to education, Mathematics on the web, Workshop CTU 2002.

2001

I. P., H.Špačková, Časově-frekvenční analýza zvuku, sborník Konference MATLAB 2001, Praha

2000

I. P., H.Špačková, Časově-frekvenční analýza zvukového souboru, sborník Konference MATLAB 2000, Praha

Conferences etc.

Implicitly constituted materials: Modeling, analysis, and computing 2013, November 24 - 27, Liblice.
Equadiff 2013, August 26 - 30, Prague.
Preconditioning of Iterative Methods, PIM 2013, July 1 - 5, 2013, Praha, (organizing committee, chair).
Finite Elements in Science and Technology, FEIST2013, June 20 - 22, 2013, Prague.
MAFELAP, June 11 - 14, 2013, Brunel University, Uxbridge.
SVOC 2013, Opava.
Applications of Mathematics 2013, May 15 - 17, 2013, Prague.
SNA 2013, January 21-25, 2013, Rožnov pod Radhoštěm, Czech Republic.
SPOMECH Workshop 2012, November 19 - 23, 2012, Ostrava.
Computer Aspects of Numerical Algorithms (CANA'12), Wrocław, Poland, September 9-12, 2012, (program committee).
XII GAMM Workshop on Applied and Numerical Linear Algebra with Special Emphasis on Adaptivity, September 2-5, 2012, Chateau Liblice, Czech Republic.
European Multigrid Conference 2012, August 13 - 16, 2012, Schwetzingen Castle, Germany.
Computational Methods in Applied Mathematics (CMAM-5), July 30 - August 3, 2012, Berlin, Germany.
SIAM Conference on Applied Linear Algebra, June 18-22, Valencia, Spain.
Seminar PANM 2012, June 3-8, 2012, Dolni Maxov.
83rd Annual Meeting of the International Association of Applied Mathematics and Mechanics, March 26-30, 2012, Darmstadt, Germany.
SNA 2012, January 23-27, 2012, Liberec.
SPOMECH Workshop 2011, November 22-24, 2011, Ostrava.
Mat Triad 2011, July 12-16, 2011, Tomar, Portugal.
Computer Aspects of Numerical Algorithms (CANA'11), September 19-21, 2011, Szczecin, Poland, (program committee).
International Conference On Preconditioning Techniques For Scientific And Industrial Applications, May 16-18, 2011 Bordeaux, France.
SNA 2011, January 24-28, 2010, Rožnov pod Radhoštěm, Czech Republic.
The Computer Aspects of Numerical Algorithms Workshop (CANA'10), October 18-20, 2010, Wisla, Poland, (program committee).
Numerical Solution of Markov Chains, September 16-17, 2010, Williamsburg, Virginia, USA, (program committee).
ESCO 2010, June 28 - July 2, 2010, Pilsen, Czech Republic.
SNA 2010, January 18-22, 2010, Nove Hrady, Czech Republic.
POSTA 2009, September 2-4, 2009, Valencia, Spain.
Modelling 2009, June 22 - 26, 2009, Roznov pod Radhostem.
MAFELAP 2009, June 9-12, 2009, Brunel University.
SNA 2009, February 2-6, 2009, Ostrava.
The 3rd International Workshop on Tools for solving Structured Markov Chains (SMCTools 2008), Athens, Greece, October 20, 2008, (program committee).
Iterative aggregation - disaggregation methods and Tarjan's algorithm, Applied Linear Algebra 2008 - in honor of Ivo Marek, (GAMM, ALA 2008), Novi Sad, April 28-30, 2008.
Hierarchical bases on rectangles, SNA'08, Seminář numerické analýzy, Modelování a simulace náročných technických problémů, 28. 1. - 1. 2. 2008, Liberec.
2007 International Conference On Preconditioning Techniques For Large Sparse Matrix Problems In Scientific And Industrial Applications , 2007, Météopole, Toulouse, France.
A Posteriori Error Estimates for Hierarchical Finite Elements, submitted to the Harrachov 2007 Conference on Computational Methods with Applications.
Energy Based A Posteriori Error Estimates for Elliptic Problems and Bilinear Hierarchical Bases, submitted to LSSC'07, Sozopol.
Convergence Issues of Some Classes of Iterative Aggregation-Disaggregation Methods in Computing Markov Chains, GAMM - SIAM Conference, Dusseldorf, Germany, July 2006.
Convergence issues of some classes of IAD methods in computing Markov chains, IWMS 2006, Uppsala, Sweden, June 2006.
IAD metody v počítání Markovových řetězců, Seminar on Numerical Analysis, 2006, Prčice, (in Czech), pdf.
Sparsity pattern for divergent IAD methods, ILAS Conference 2005, Regina, Saskatchewan, June 2005, pdf.
Google search engine - some computing experience, Seminar on Numerical Analysis, Modelling and Simulation of Challenging Engineering Problems, Ostrava, 2005.
Global Convergence for Iterative Aggregation-Disaggregation Method, ERCIM 2004, Prague, August 29, 2004.
Threshold Partitioning for Iterative Aggregation-Disaggregation Method, ILAS 2004, Coimbra, July 22, 2004.

Books and lecture notes

J. Novák, I. P., P. Novák, Základy informatiky – počítačové modelování v MATLABU. Česká technika - nakladatelství ČVUT (CTN) 2005.
I. P., M. Pultar, Úvod do systému Windows 2000. Doplňkové skriptum. Vydavatelství ČVUT 2000. Elektronická verze (3.54 MB).
F. Bubeník, M. Pultar, I. P., Matematické vzorce a metody. Vydavatelství ČVUT 1994, 1997. New edition 2010.

Grants

GAČR 201/09/P500, 2009 - 2010
MSM6840770001 - Spolehlivost, optimalizace a trvanlivost stavebních materiálů a konstrukcí, Katedra matematiky, Fakulta stavební, 2005-2011
CTU CTU0400111 - Víceúrovňová aditivní a multiplikativní Schwarzova metoda (Multilevel additive and multiplikative Schwarz method), Katedra matematiky, Fakulta stavební, 2004
CTU CTU0300111 - Víceúrovňové řešení úloh s rychle se měnícími vlastnostmi (Multilevel treatment of some problems with fast changing data), Katedra matematiky, Fakulta stavební, 2003
Participating in
GAČR 201/09/1544, 2009 - 2011,
GAČR 201/02/0597, 2002-2004,
GAČR 201/05/0453, 2005-2007,
MŠMT 1ET400300415, 2004-2008,
MŠMT MSM 210000001, 2003-2004.

Rue Des Cascades, sem MU