Publications

Journals

  • I. Hnětynková, M. Plešinger, J. Žáková: On TLS formulation and core reduction for data fitting with generalized models, in Linear Algebra and Its Applications 577, pp. 1-20 (2019).
  • I. Hnětynková, M. Plešinger, J. Žáková: Solvability classes for core problems in matrix total least squares minimization, in Applications of Mathematics 64(2), pp. 103-128 (2019).
  • I. Hnětynková, P. Tichý: Characterization of half-radial matrices, in Linear Algebra and Its Applications 559, pp. 227-243 (2018).
  • I. Hnětynková, M. Plešinger, J. Žáková: TLS formulation and core reduction for problems with structured right-hand sides, in Linear Algebra and Its Applications 555, pp. 241-265 (2018).
  • I. Hnětynková, M. Plešinger, J. Žáková: Filter factors of truncated TLS regularization with multiple observations, in Applications of Mathematics 62, pp. 105-120 (2017).
  • I. Hnětynková, M. Kubínová, M. Plešinger: Noise representation in residuals of CRAIG, LSQR and LSMR regularization, in Linear Algebra and Its Applications 533, pp. 357-379 (2017).
  • I. Hnětynková, M. Plešinger, D. Sima: Solvability of the core problem with multiple right-hand sides in the TLS sense, in SIAM J. on Matrix Anal. and Appl. 37, pp. 861-876 (2016).
  • I. Hnětynková, M. Plešinger, Z. Strakoš: Band generalization of the Golub-Kahan bidiagonalization, generalized Jacobi matrices, and the core problem, in SIAM J. on Matrix Anal. and Appl. 36, pp. 417–434 (2015).
  • I. Hnětynková, M. Plešinger: Complex wedge-shaped matrices: A generalization of Jacobi matrices, in Linear Algebra and Its Applications 487, pp. 203-219 (2015).
  • I. Hnětynková, M. Plešinger, Z. Strakoš: The core problem within a linear approximation problem AX~B with multiple right-hand sides, in SIAM J. on Matrix Anal. and Appl. 34, pp. 917-931 (2013).
  • I. Hnětynková, M. Plešinger, D. Sima, Z. Strakoš, S. Van Huffel: The total least squares problem in AX~ B. A new classification with the relationship to the classical works, in SIAM J. on Matrix Anal. and Appl. 32, pp. 748-770 (2011).
  • R. A. Renaut, I. Hnětynková, J. Mead: Regularization parameter estimation for large-scale Tikhonov regularization using a priori information, in Computational Statistics and Data Analysis 54, pp. 3430-3445 (2010).
  • I. Hnětynková, M. Plešinger, Z. Strakoš: The regularizing effect of the Golub-Kahan iterative bidiagonalization and revealing the noise level in the data, in BIT Numerical Mathematics 49, pp. 669-696 (2009).
  • I. Hnětynková, Z. Strakoš: Lanczos tridiagonalization and core problems, in Linear Algebra and Its Applications 421, pp. 243-251 (2007).

Text book

  • J. Duintjer Tebbens, I. Hnětynková, M. Plešinger, Z. Strakoš, P. Tichý: Analysis of Methods for Matrix Computations: Basic Methods, Matfyzpress, Prague, ISBN 978-80-7378-201-6, 2012, 328 p.

Peer-reviewed conference proceedings

  • I. Hnětynková, M. Plešinger, J. Žáková: Towards tensor generalizations of TLS & core theory, in PAMM 18 - Special Issue: 89th Annual Meeting of the International Association of Applied Mathematics and Mechanic, Munich, WILEY-VCH Verlag, pp. 1-2 (2018).
  • I. Hnětynková, M. Kubínová, T. Gergelits: Relating computed and exact entities in methods based on Lanczos tridiagonalization, in High Performance Computing in Science and Engineering HPCSE 2017, Kozubek T. et al. (eds), Lecture Notes in Computer Science 11087, pp. 73-87 (2018).
  • I. Hnětynková, M. Plešinger, J. Žáková: Modification of TLS algorithm for solving F2 linear data fitting problems, in PAMM 17 - Special Issue: 88th Annual Meeting of the International Association of Applied Mathematics and Mechanic, Weimar and Ilmenau, WILEY-VCH Verlag, pp. 749-750 (2017).
  • I. Hnětynková, M. Kubínová, M. Plešinger: Notes on performance of bidiagonalization-based estimator in image deblurring, in Proceedings of Algoritmy 2016 - 20th Conference on Scientific Computing, Vysoké Tatry - Podbanské, Publishing House of Slovak University of Technology, pp. 333 - 342 (2016).
  • I. Hnětynková, M. Plešinger, Z. Strakoš: On solution of total least squares problem with multiple right-hand sides, in PAMM 8 - Special Issue: 79th Annual Meeting of the International Association of Applied Mathematics and Mechanics, Bremen, WILEY-VCH Verlag, pp. 10815-10816 (2009).
  • I. Hnětynková, M. Plešinger, Z. Strakoš: Lanczos tridiagonalization, Golub-Kahan bidiagonalization and core problem, in PAMM 6 - Special Issue: GAMM Annual Meeting 2006, Berlin, WILEY-VCH Verlag, pp. 717-718 (2006).
  • J. Zítko, I. Ulrychová: Iterative technique for construction of invariant subspace, in PAMM 5 - Special Issue: GAMM Annual Meeting 2005, Luxembourg, WILEY-VCH Verlag, pp. 801-802 (2005).

Other conference proceedings

  • I. Hnětynková, M. Plešinger, D. Sima, Z. Strakoš, S. Van Huffel: The core problem within a linear approximation problem with multiple right-hand sides, in Proceedings of SNA'14 - Modelling and Simulation of Challenging Engineering Problems, Nymburk, pp. 44-45 (2014).
  • M. Kubínová, I. Hnětynková: Noise revealing in Golub-Kahan bidiagonalization as a mean of regularization in discrete inverse problems, in Proceedings of SNA'14 - Modelling and Simulation of Challenging Engineering Problems, Nymburk, pp. 62 – 64 (2014).
  • J. Kuřátko, I. Hnětynková: Calculating the rank of the Sylvester matrix, in Proceedings of SNA'12 - Modelling and Simulation of Challenging Engineering Problems, Liberec, pp. 121 – 124 (2012).
  • I. Hnětynková, M. Plešinger, Z. Strakoš: Golub-Kahan iterative bidiagonalization and stopping criteria in ill-posed problems, in Proceedings of SNA'07 - Modelling and Simulation of Challenging Engineering Problems, Ostrava, pp. 41-45 (2007).
  • M. Plešinger, I. Hnětynková, D. Sima, Z. Strakoš: Total least squares problems in linear algebraic systems with multiple right-hand sides, in Proceedings of SNA'07 - Modelling and Simulation of Challenging Engineering Problems, Ostrava, pp. 81-84 (2007).
  • I. Hnětynková, Z. Strakoš: Lanczos tridiagonalization, Golub-Kahan bidiagonalization and the core problem, in Proceedings of SNA'06 - Modelling and Simulation of Challenging Engineering Problems, Moninec, pp. 37-42 (2006).
  • J. Zítko, I. Hnětynková: Behaviour of IRA iterations for derogatory and defective matrices, in Proceedings of SNA´06 - Modelling and Simulation of Challenging Engineering Problems, Moninec, pp. 105-108 (2006).
  • I. Ulrychová, J. Zítko: Construction of invariant subspaces and their application for improving GMRES(m) method, in Proceedings of SNA´05 - Modelling and Simulation of Challenging Engineering Problems, Ostrava, pp. 83-86 (2005).
  • I. Ulrychová, J. Zítko: Polynomial filters and their applications, in Proceedings of the XIII. Annual Conference of Doctoral Students WDS´04, Prague, pp. 118-123 (2004).

Theses

  • I. Hnětynková: Krylov subspace approximations in linear algebraic problems, Doctoral thesis, Charles University, Czech Republic, 2006
  • I. Hnětynková: Acceleration of convergence of the GMRES method, Master thesis, Charles University, Czech Republic, 2003