Petr Tichý
Department of Numerical Mathematics
Sokolovska 83, 18675 Praha 8, Czech Republic

Publications

submitted
  • G. Meurant, J. Papež, and P. Tichý, Accurate error estimation in CG, submitted, January 11, 2021.
    [arXiv
published papers
  • C. Echeverría, J. Liesen, and P. Tichý, Analysis of the multiplicative Schwarz method for matrices with a special block structure, Electronic Transactions on Numerical Analysis (ETNA), Volume 54, pp. 51-67, 2021.
    [arXiv]  [DOI]  [presentation]  [journal]  [MathSciNet
  • V. Dolejší and P. Tichý, On efficient numerical solution of linear algebraic systems arising in goal-oriented error estimates,, Journal of Scientific Computing (JOMP), Volume 83, Issue 1, 2020.
    [arXiv]  [DOI]  [journal]  [MathSciNet
  • G. Meurant and P. Tichý, Approximating the extreme Ritz values and upper bounds for the A-norm of the error in CG, Numerical Algorithms, Volume 82, Issue 3, pp 937-968, November 2019.
    [arXiv]  [DOI]  [presentation]  [journal]  [MathSciNet
  • E. Carson, M. Rozložník, Z. Strakoš, P. Tichý, and M. Tůma, The numerical stability analysis of pipelined conjugate gradient methods: Historical context and methodology, SIAM Journal on Scientific Computing, Volume 40, Issue 5, pp. A3549-A3580, 2018.
    [pdf]  [DOI]  [journal]  [MathSciNet
  • I. Hnětynková and P. Tichý, Characterization of half-radial matrices, Linear Algebra and its Applications, Volume 559, pp. 227-243, 2018.
    [pdf]  [DOI]  [journal]  [presentation]  [MathSciNet
  • C. Echeverría, J. Liesen, D. B. Szyld, P. Tichý, Convergence of the multiplicative Schwarz method for singularly perturbed convection-diffusion problems discretized on a Shishkin mesh, Electronic Transactions on Numerical Analysis (ETNA), Volume 48, pp. 40-62, 2018.
    [pdf]  [DOI]  [journal]  [presentation]  [MathSciNet
  • J. Liesen and P. Tichý, Max-min and min-max approximation problems for normal matrices revisited, Electronic Transactions on Numerical Analysis (ETNA), Volume 41, pp. 159-166, 2014.
    [pdf]  [journal]  [presentation]  [MathSciNet
  • V. Faber, J. Liesen and P. Tichý, Properties of worst-case GMRES, SIAM Journal on Matrix Analysis and Applications, Volume 34, Issue 4, pp. 1500-1519, 2013.
    [pdf]  [DOI]  [arXiv]  [presentation]  [MathSciNet
  • G. Meurant and P. Tichý, On computing quadrature-based bounds for the A-norm of the error in conjugate gradients, Numerical Algorithms, Volume 62, Issue 2, pp. 163-191, 2013.
    [pdf]  [DOI]  [journal]  [presentation]  [MathSciNet erratum: [pdf]  [DOI
  • Z. Strakoš and P. Tichý, On efficient numerical approximation of the bilinear form c*A-1b , SIAM Journal on Scientific Computing, Volume 33, Issue 2, pp. 565-587, 2011.
    [pdf]  [DOI]  [journal]  [presentation]  [MathSciNet
  • V. Faber, J. Liesen and P. Tichý, On Chebyshev polynomials of matrices, SIAM Journal on Matrix Analysis and Applications, Volume 31, Issue 4, pp. 2205-2221, 2010.
    [pdf]  [DOI]  [journal]  [presentation]  [MathSciNet
  • J. Liesen and P. Tichý, On best approximations of polynomials in matrices in the matrix 2-norm, SIAM Journal on Matrix Analysis and Applications, Volume 31, Issue 2, pp. 853-863, 2009.
    [pdf]  [DOI]  [journal]  [presentation]  [MathSciNet
  • V. Faber, J. Liesen and P. Tichý, On orthogonal reduction to Hessenberg form with small bandwidth, Numerical Algorithms, Volume 51, pp. 133-142, 2009.
    [pdf]  [DOI]  [journal]  [MathSciNet
  • V. Faber, J. Liesen and P. Tichý, The Faber-Manteuffel theorem for linear operators, SIAM Journal on Numerical Analysis, Volume 46, pp. 1323-1337, 2008.
    [pdf]  [DOI]  [journal]  [MathSciNet]  [presentation
  • P. Tichý, J. Liesen and V. Faber, On worst-case GMRES, ideal GMRES, and the polynomial numerical hull of a Jordan block, Electronic Transactions on Numerical Analysis (ETNA), Volume 26, pp. 453-473, 2007.
    [pdf]  [journal]  [MathSciNet]  [presentation
  • D. P. O'Leary, Z. Strakoš and P. Tichý, On sensitivity of Gauss-Christoffel quadrature, Numerische Mathematik, Volume 107, pp. 147-174, 2007.
    [pdf]  [DOI]  [journal]  [MathSciNet]  [ZentralBlatt MATH
  • Z. Strakoš and P. Tichý, Error Estimation in Preconditioned Conjugate Gradients, BIT Numerical Mathematics, Volume 45, pp. 789-817, 2005.
    [pdf]  [DOI]  [journal]  [MathSciNet]  [ZentralBlatt MATH]  [presentation
  • J. Liesen and P. Tichý, On the worst-case convergence of MR and CG for symmetric positive definite tridiagonal Toeplitz matrices, Electronic Transactions on Numerical Analysis (ETNA), Volume 20, pp. 180-197, 2005.
    [pdf]  [journal]  [MathSciNet]  [ZentralBlatt MATH]  [presentation
  • J. Liesen and P. Tichý, Convergence analysis of Krylov subspace methods, GAMM Mitteilungen, Band 27, Heft 2, 2004.
    [pdf]  [journal]  [MathSciNet]  [ZentralBlatt MATH
  • J. Liesen and P. Tichý, The worst-case GMRES for normal matrices , BIT Numerical Mathematics, Volume 44, pp. 79-98, 2004.
    [pdf]  [DOI]  [journal]  [MathSciNet]  [ZentralBlatt MATH]  [presentation
  • Z. Strakoš and P. Tichý, On Error Estimation in the Conjugate Gradient Method and Why It Works In Finite Precision Computations, Electronic Transactions on Numerical Analysis (ETNA), Volume 13, pp. 56-80, 2002.
    [pdf]  [journal]  [MathSciNet]  [ZentralBlatt MATH]  [presentation
  • P. Tichý and J. Zítko, Derivation of BiCG from the conditions defining Lanczos' method for solving a system of linear equations, Application of Mathematics 5, (43), pp. 381--388, 1998.
    [ps-file]  [DOI]  [journal]  [MathSciNet]  [ZentralBlatt MATH
textbook
  • J. Duintjer Tebbens, I. Hnetynkova, M. Plesinger, Z. Strakos and P. Tichy, Analysis of methods for matrix computations, Basic methods(in Czech ), Matfyzpress Prague, ISBN 978-80-7378-201-6, 2012, 328 p.
    [book site]  [Publisher Matfyzpress
technical reports and preprints
  • J. Liesen and P. Tichý, The Field of Values Bounds on Ideal GMRES, arXiv:1211.5969, 2018.
    [pdf]  [presentation]  [arXiv]
  • Tichý, P. and Liesen, J., GMRES convergence and the polynomial numerical hull for a Jordan block, Preprint 34-2006, Institute of Mathematics, Technische Universität Berlin, 2006.
    abstract  pdf  presentation  institute 
  • Tichý, P. and  Liesen, J., Worst-case and ideal GMRES for a Jordan block, Preprint 19-2005, Institute of Mathematics, Technische Universität Berlin, 2005.
    abstract  pdf  institute 
  • Liesen, J. and Tichý, P., Behavior of CG and MINRES for symmetric tridiagonal Toeplitz matrices, Preprint 34-2004, Institute of Mathematics, Technische Universität Berlin, 2004.
    abstract  pdf  institute 
  • Liesen, J. and Tichý, P., A min-max problem on roots of unity, Preprint 28-2003, Institute of Mathematics, Technische Universität Berlin, 2003.
    abstract  pdf  institute 
conference publications
  • Tichý, P., On Error Estimation in the Conjugate Gradient Method: Normwise Backward Error, Proceedings of Algoritmy 2016, pp. 323-332, 2016.
    pdf  conference 
  • Meurant, G. and Tichý, P., A new algorithm for computing quadrature-based bounds in CG, Book of Abstracts - Householder Symposium XIX, pp. 224-225, 2014.
    pdf  conference 
  • Faber, V. and Liesen, J. and Tichý, P., On best approximation by polynomials of matrices, Book of Abstracts - Householder Symposium XVIII, pp. 231-232, 2011.
    pdf  conference 
  • Faber, V. and Liesen, J. and Tichý, P., On a New Proof of the Faber-Manteuffel Theorem, Book of Abstracts - Householder Symposium XVII, pp. 158-160, 2008.
    pdf  conference 
  • Tichý, P. and Liesen, J., Worst-case and Ideal GMRES for a Jordan Block, Abstracts - Householder Symposium XVI, pp. 226-228, 2005.
    pdf  conference 
  • Liesen, J. and Tichý, P., The worst-case GMRES for normal matrices, In Proceedings of IMET 2004 - Iterative Methods, Preconditioning & Numerical PDEs, pages 113-116, 2004.
    pdf 
  • Strakoš, Z. and Tichý, P., On Estimation of the A-norm of the Error in CG and PCG, PAMM, Volume 3, Issue 1, pp. 553-554, 2003.
    abstract  pdf 
  • Tichý, P., The shadow vector in the Lanczos Method, Proceedings of the XUIIth summer school software and algorithms of numerical mathematics Nečtiny, pp. 309-320, 1999.
    pdf 
thesis

update 12.01.2021