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Publications

books G. Meurant and P. Tichý, Error Norm Estimation in the Conjugate Gradient Algorithm, SIAM Spotlights, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2024, x+127 p. [DOI]  [SIAM Spotlights] J. Duintjer Tebbens, I. Hnětynková, M. Plešinger, Z. Strakoš and P. Tichý, Analýza metod pro maticové výpočty , Matfyzpress, Prague, ISBN 978-80-7378-201-6, 2012, 328 p. [Publisher Matfyzpress]  in the process G. Meurant and P. Tichý, Error norm estimates for the block conjugate gradient algorithm, submitted, February, 2025. [arXiv]  papers P. Tichý, G. Meurant, and D. Šimonová, Block CG algorithms revisited, Numerical Algorithms, published online, March 2025. [arXiv]  [DOI]  [journal]  J. Papež and P. Tichý, Estimating error norms in CG-like algorithms for least-squares and least-norm problems, Numerical Algorithms, Vol. 97, No. 1, pp. 1-28, 2024. [arXiv]  [DOI]  [presentation]  [journal]  [MathSciNet]  V. Faber, J. Liesen and P. Tichý, On the Forsythe conjecture, BIT Numerical Mathematics, Vol. 63(4), 2023. [arXiv]  [DOI]  [presentation]  [journal]  [MathSciNet]  G. Meurant and P. Tichý, The behaviour of the Gauss-Radau upper bound of the error norm in CG, Numerical Algorithms, Vol. 94, pp. 847-876, 2023. [arXiv]  [DOI]  [presentation]  [journal]  [MathSciNet]  D. Šimonová and P. Tichý, When does the Lanczos algorithm compute exactly? Electronic Transactions on Numerical Analysis (ETNA), Volume 55, pp. 547-567, 2022. [arXiv]  [DOI]  [journal]  [MathSciNet]  G. Meurant, J. Papež, and P. Tichý, Accurate error estimation in CG, Numerical Algorithms, Volume 88, pp. 1337-1359, 2021. [arXiv]  [DOI]  [presentation]  [journal]  [MathSciNet]  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. Knizek, P. Tichy, L. Beranek, J. Sindelar, B. Vojtesek, P. Bouchal, R. Nenutil, O. Dedik Note on generating orthogonal polynomials and their application in solving complicated polynomial regression tasks International Journal of Mathematics and Computation, Volume 7, Number J10, pp. 48-60, 2010. [journal]  [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]  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 Tichý, P., O některých otevřených problémech v krylovovských metodách (On Some Open Questions In Krylov Subspace Methods), Ph.D. thesis, Department of Numerical Mathematics, Faculty of Mathematics and Physics, 114 p., Praha 2002. Tichý, P., On Some Open Questions In Krylov Subspace Methods, Summary of Ph.D thesis, Department of Numerical Mathematics, Faculty of Mathematics and Physics, 12 p., Praha 2002. Tichý, P., Chování BiCG a CGS algoritmů (Behaviour of BiCG and CGS algorithms), Master-thesis, Department of Numerical Mathematics, Faculty of Mathematics and Physics, Praha 1997.