Publications

Gergelits Tomáš, Nielsen Bjørn F., and Strakoš Zdeněk: Generalized spectrum of second order differential operators to appear in SIAM Journal on Numerical Analysis. [download the preprint]

Gergelits Tomáš, Mardal Kent-Andre, Nielsen Bjørn F., and Strakoš Zdeněk: Laplacian preconditioning of elliptic PDEs: Localization of the eigenvalues of the discretized operator. SIAM Journal on Numerical Analysis, 57, 2019, pp. 1369 - 1394. [download the preprint]

Gergelits Tomáš, Hnětynková Iveta, and Kubínová Marie: Relating computed and exact entities in methods based on Lanczos tridiagonalization. in Proceedings of High Performance Computing in Science and Engineering 2017, Lecture Notes in Computer Science, Springer. [download the preprint]

Gergelits Tomáš, and Strakoš Zdeněk: Composite convergence bounds based on Chebyshev polynomials and finite precision conjugate gradient computations. Numerical Algorithms 65 (4). pp. 759–782. 2014. [download the preprint]

Presentations

Conferences abroad

Relating computed and exact entities in Krylov subspace methods based on short recurrences. GAMM Annual Meeting 2018. Munich, Germany. March 2018.[slides]

Rank deficiency and nearness to Krylov subspaces in finite precision computations. 27th Biennial Conference on Numerical Analysis. Strathclyde, Scotland, United Kingdom. June 2017.

Estimation of Algebraic and Total Error in Diffusion Equations with Random Coefficients. IHP quarter on Numerical Methods for PDEs. Paris, France. October 2016.

Estimation of Algebraic and Total Error in Diffusion Equations with Random Coefficients. 5th IMA Conference on Numerical Linear Algebra and Optimisation. University of Birmingham, UK. September 2016.

Properties of Krylov subspace methods based on short recurrences in finite precision computations ILAS 2016. Leuven, Belgium. July 2016.[slides]

Interpretation of algebraic preconditioning as transformation of the discretization basis. SIAM Conference on Applied Linear Algebra 2015. Atlanta, Georgia, USA. October 2015.[slides]

Properties of the CG method in finite precision computations CIME Summer School 2015. Cetraro, Italy. June 2015.[slides]

On the numerical behaviour of the CG method Student Krylov Day 2015. TU Delft, Netherlands. February 2015.[slides]

On the properties of Krylov subspaces in finite precision CG computations. 4th IMA Conference on Numerical Linear Algebra and Optimisation. University of Birmingham, UK. September 2014.[slides]

Composite polynomial convergence bounds in finite precision CG computations. ENUMATH 2013. EPFL Lausanne, Switzerland. August 2013.[slides]

Conferences in the Czech Republic

On the properties of Krylov subspaces in finite precision CG computations. MORE Conference: Modeling, analysis and computing in nonlinear PDEs. Liblice, Czech Republic. September 2014. [poster], [video on SlidesLive.com]

Tracking the trajectory in finite precision CG computations. SNA 2014: Seminar of numerical analysis and winter school. Nymburk, Czech Republic. January 2014.[slides]

Tracking the trajectory in finite precision CG computations. MORE Workshop: Implicitly constituted materials: Modeling, analysis, and computing . Liblice, Czech Republic. January 2014.[poster]

Composite polynomial convergence bounds, the CSI method and finite precision CG computations. SNA 2013: Seminar of numerical analysis and winter school. Roľnov pod Radhoątem, Czech Republic. January 2013.[slides]

Composite bounds of the error in FP CG computations. SNA 2012: Seminar of numerical analysis and winter school. Liberec, Czech Republic. January 2012.[poster]