Publications

[Selection of Publications] [Other Relevant Publications]

Monographs

  • J. Liesen and Z. Strakos, Krylov Subspace Methods, Principles and Analysis, Oxford University Press, ISBN 978-0-19-965541-0, 2013, 408p. Errata
  • J. Malek and Z. Strakos, Preconditioning and the Conjugate Gradient Method in the Context of Solving PDEs, SIAM Spotlight Series, SIAM, Philadelphia, ISBN 978-1-611973-83-9, 2015,  viii+104p. 

    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.

    Publications in Journals

  • S. Pozza, M. Pranic and Z. Strakos, Lanzcos algorithm and the complex Gauss quadrature, submitted for publication in May 2017[download]
  • E. Carson, M. Rozloznik, Z. Strakos, P. Tichy, and M. Tuma, On the numerical stability analysis of pipelined Krylov subspace methods, Preprint NCMM/2016/08, submitted for publication in November 2016, revised July 2017.[download]
  • J. Papez and Z. Strakos, On a residual-based a posteriori error estimator for the total error, Accepted for publication in IMA J. Numer. Anal., June 2017. [download]
  • J. Papez, Z. Strakos and M. Vohralik, Estimating and localizing the algebraic and total numerical errors using flux reconstructions, accepted for publication in Numerische Mathematik, July 2017.[download]
  • S. Pozza, M. Pranic and Z. Strakos, Gauss quadrature for quasidefinite linear functionals, IMA J. Numer. Anal., 37, 2017, pp. 1468-1495.
  • I. Hnetynkova, M. Plesinger and Z. Strakos, Band generalization of the Golub--Kahan bidiagonalization, generalized Jacobi matrices, and the core problem, SIAM J. Matrix Annal. Appl. (SIMAX), 36, 2015, pp. 417–434.[download]
  • J. Duintjer Tebbens, G. Meurant, H. Sadok, and Z. Strakos, On investigating GMRES convergence using unitary matrices, Linear Algebra and its Appl., 450, 2014, pp. 83-107. [download]
  • J. Papez, J. Liesen and Z. Strakos, Distribution of the discretization and algebraic error in numerical solution of partial differential equations, Linear Algebra Appl., 449, 2014, pp. 89-114.  [download]
  • T. Gergelits and Z. Strakos, Composite convergence bounds based on Chebyshev polynomials and finite precision conjugate gradient computations, Numerical Algorithms, 65, 2014, pp. 759-782. [download]
  • I. Hnetynkova, M. Plesinger and Z. Strakos, Core problem within linear approximation problem AX ~ B with multiple right-hand sides, SIAM J. Matrix Annal. Appl. (SIMAX), 34, 2013, pp. 917-931. [download]
  • M. Arioli, J. Liesen, A. Miedlar and Z. Strakos, Interplay between discretization and algebraic computation in adaptive numerical solution of elliptic PDE problems, GAMM Mitteilungen, 36, 2013, pp. 102-129. [download]
  • I. Hnetynkova, M. Plesinger, M. Sima, Z. Strakos and S. Van Huffel, The total least squares problem in AX approx B. A new classification with the relationship to the classical works , SIAM J. Matrix Annal. Appl. (SIMAX), 32, 2011, pp. 748-770. [download]
  • Z. Strakos, Featured Review: G. H. Golub and G. Meurant, Matrices, Moments and Quadrature with Applications, Princeton University Press, 2010 , Foundations of Computational Mathematics (FoCM), 11, 2011, pp. 241-255.
  • Z. Strakos and P. Tichy, On efficient numerical approximation of the bilinear form c*A-1b , SIAM Journal on Scientific Computing (SISC), 33, 2011, pp. 565-587. [download]
  • P. Jiranek, Z. Strakos and M. Vohralik, A posteriori error estimates including algebraic error and stopping criteria for iterative solvers , SIAM Journal on Scientific Computing (SISC), 32, 2010, pp. 1567-1590. [download]
  • I. Hnetynkova, M. Plesinger and Z. Strakos, Golub-Kahan iterative bidiagonalization and determining the size of the noise in data , BIT Numerical Analysis, 49, 2009, pp. 669-696. [download] The original publication is available on LINK at http://link.springer.de © Springer-Verlag.
  • J. Hench and Z. Strakos, The RCWA method - a case study with open questions and perspectives of algebraic computations , ETNA, 31, 2009, pp. 331-357. The original publication is available on link at http://etna.mcs.kent.edu/ © ETNA. [download]
  • Z. Strakos, Model reduction using the Vorobyev moment problem , Numerical Algorithms, 51, 2009, pp. 363-379. [download] The original publication is available on LINK at http://link.springer.de © Springer-Verlag.
  • J. Liesen and Z. Strakos, On optimal short recurrences for generating orthogonal Krylov subspace bases , SIAM Review, 50, 2008, pp. 485-503. [download]
  • D. P. O'Leary, Z. Strakos and P. Tichy, On Sensitivity of Gauss-Christoffel quadrature , Numerische Mathematik, 107, 2007, pp. 147 --174. [download] The original publication is available on LINK at http://link.springer.de © Springer-Verlag.
  • I. Hnetynkova and Z. Strakos, Lanczos tridiagonalization and core problems , Linear Algebra Appl., 421, 2007, pp. 243-251. [download]
  • G. Meurant and Z. Strakos, The Lanczos and conjugate gradient algorithms in finite precision arithmetic , Acta Numerica, 15, Cambridge University Press, 2006, pp. 471-542. [download]
  • C.C. Paige, M. Rozloznik and Z. Strakos, Modified Gram-Schmidt (MGS), Least Squares, and Backward Stability of MGS-GMRES, SIAM J. Matrix Anal. Appl., 28, 2006, pp. 264-284. [download]
  • C.C. Paige and Z. Strakos, Core Problems in Linear Algebraic Systems, SIAM J. Matrix Anal. Appl., 27, 2006, pp. 861-875 [download]
  • Z. Strakos and P. Tichy, Error Estimation in Preconditioned Conjugate Gradients , BIT Numerical Mathematics, 45, 2005, pp. 789-817. The original publication is available on LINK at http://link.springer.de © Springer-Verlag. [download]
  • J. Liesen and Z. Strakos, GMRES Convergence Analysis for a Convection-Diffusion Model Problem, SIAM J. on Scientific Computing, 26, 2005, pp. 1989-2009. [download]
  • Z. Strakos and J. Liesen, On Numerical Stability in Large Scale Linear Algebraic Computations , Zeitschrift fuer Angewandte Mathematik und Mechanik, 85, 5, 2005, pp. 307-325.
  • J. Liesen and Z. Strakos, Convergence of GMRES for Tridiagonal Toeplitz Matrices, SIAM J. Matrix Anal. Appl., 26, 2004, pp. 233-251. [download]
  • Z. Strakos and P. Tichy, 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, published online, 2002. The original publication is available on link at http://etna.mcs.kent.edu/ © ETNA. [download]
  • J. Liesen, M. Rozloznik and Z. Strakos, Least Squares Residuals and Minimal Residual Methods, SIAM J. Sci. Comput. 23, 5, 2002,  pp. 1503-1525. [download]
  • C.C. Paige and Z. Strakos, Bounds for the Least Squares Distance using Scaled Total Least Squares Problems, Numerische Mathematik, 91, 2002, pp. 93-115, published online July 25, 2001. The original publication is available on LINK at http://link.springer.de © Springer-Verlag. [download]
  • C.C. Paige and Z. Strakos, Scaled Total Least Squares Fundamentals, Numerische Mathematik, 91, 2002, pp. 117-146, published online July 25, 2001. The original publication is available on LINK at http://link.springer.de © Springer-Verlag. [download]
  • C.C. Paige and Z. Strakos, Residual and Backward Error Bounds in Minimum Residual Krylov Subspace Methods, SIAM J. Sci. Comput. 23, 6, 2002, pp. 1899-1924. [download]
  • M. H. Gutknecht and Z. Strakos, Accuracy of Two Three-Term and Three Two-Term Recurrences for Krylov Space Solvers, SIAM J. Matrix Anal. Appl. 22, 1, Jan. 2001, pp. 213--229.
  • M. Arioli, V. Ptak and Z. Strakos, Krylov Sequences of Maximal Length and Convergence of GMRES, BIT 38 (1998), pp. 636--643.
  • Bjorck, A., Elfving, T. and Strakos, Z. Stability of Conjugate Gradient and Lanczos Methods for Linear Least Squares Problems , SIAM J. Matrix Anal. Appl. 19, 3, July 1998, pp. 720 -736.
  • Greenbaum, A., Rozloznik, M. and Strakos, Z. Numerical Behaviour of the Modified Gram-Schmidt GMRES Implementation, BIT 37 (1997), pp. 706 - 719.
  • Greenbaum, A., Ptak, V. and Strakos, Z. Any Convergence Curve is Possible for GMRES, SIAM Matrix Anal. Appl. 17, 3, June 1996, pp. 465-470.
  • Drkosova, J., Greenbaum A., Rozloznik M. and Strakos Z. Numerical Stability of GMRES Method, BIT 35, 1995, pp. 308 - 330.
  • Golub, G.H. and Strakos, Z. Estimates in Quadratic Formulas, Numerical Algorithms 8, 1994, pp. 241 -268.
  • Greenbaum, A. and Strakos, Z. Predicting the Behavior of Finite Precision Lanczos and Conjugate Gradient Computations, SIAM J. Matrix Anal. Appl. 13, 1, Jan. 1992, pp. 121-137.
  • Strakos, Z. On the Real Convergence Rate of the Conjugate Gradient Method, Lin. Alg. Appl. 154-156, Sep. 1991, pp. 535-549.
  • Havranek, T. and Strakos, Z. On practical Experience With Paralel Processing of Linear Models. Bulletin of the International Statistical Institute, Vol. 53, 1989, pp. 105-117.
  • Strakos, Z. Effectivity and Optimizing of Algorithms and Programs on the Host Computer / Array Processor System, Parallel Computing, 4, 1987, pp. 189-209.
  • Strakos, Z. Performance of the EC2345 Array Processor, Computers and Artificial Intelligence, Vol.4, 1985, pp.373-384.
  • Selection of Other Publications

  • I. Hnetynkova, M. Plesinger and Z. Strakos, On Solution of Total Least Squares Problems with Multiple Right-hand Sides, , PAMM, 8, 1, 2008, pp. 10815-1081.
  • Z. Strakos, Numerical linear algebra and some problems in computational statistics , Proceedings of IASC2008, Yokohama, December 2008, JSCS, pp. 1469-1478. [download]
  • I. Hnetynkova, M. Plesinger and Z. Strakos, Lanczos tridiagonalization, Golub-Kahan bidiagonalization and core problem , PAMM, 6, 1, 2006, 717-718. [download]
  • Z. Strakos and P. Tichy, On Estimation of the A-norm of the Error in CG and PCG , PAMM, 3, 1, 2003, pp. 551-552.
  • J. Liesen and Z. Strakos, Slow Initial Convergence of GMRES for SUPG Discretized Convection-Diffusion Problems, PAMM, 3, 1, 2003, pp. 553-554.
  • C.C. Paige and Z. Strakos, Bounds for the Least Squares Residual Using Scaled Total Least Squares, In: Proceedings of the Third International Workshop on TLS and Errors-in-Variables Modelling, S. Van Huffel and P. Lemmerling (eds.), Kluwer Academic, Doordrecht, 2001, pp. 25-34. [download]
  • C.C. Paige and Z. Strakos, Unifying Least Squares, Total Least Squares and Data Least Squares Problems, In: Proceedings of the Third International Workshop on TLS and Errors-in-Variables Modelling, S. Van Huffel and P. Lemmerling (eds.), Kluwer Academic, Doordrecht, 2001, pp. 35-44. [download]
  • Z. Strakos, Theory of Convergence and Effects of Finite Precision Arithmetic in Krylov Subspace Methods (D. Sc. Thesis), AS CR, 104+156p., Prague, Febr. 2001.
  • J. Nagy and Z. Strakos, Enforcing Nonnegativity in Image Reconstruction Algorithms, in: Mathematical Modelling, Estimation and Imaging, D.C. Wilson et. al., eds., SPIE Proceedings Series, Volume 4121, 2000, pp. 182--190.
  • C.C. Paige and Z. Strakos, Correspondence between Exact Arithmetic and Finite Precision Behaviour of Krylov Space Methods, (extended abstract)  The Householder Symposium on Numerical Linear Algebra), 1999, pp. 250-253. [download]
  • Strakos, Z, Convergence and Numerical Behaviour of the Krylov Space Methods, in: Proceedings of the NATO ASI Institute Algorithms for Large Sparse Linear Algebraic Systems: The State of the Art and Applications in Science and Engineering, G. Winter Althaus and E. Spedicato eds., Kluiwer Academic, 1998, pp. 175 - 197.
  • Rozloznik, M., Strakos, Z. and Tuma, M. On the Role of Orthogonality in the GMRES Method, In: Proceedings of SOFSEM'96, Lecture Notes in Computer Science, Vol. 1175, Springer, 1996, pp. 409 - 416.
  • Drkosova, J. and Strakos, Z. Introduction to Perturbation and Stability Theory in Numerical Linear Algebra (lecture notes), Czech Technical University, Prague, 1996 (in Czech).
  • Rozloznik, M. and Strakos, Z. On the Implementation of Some Residual Minimizing Krylov Space Methods, In: Proceedings of SOFSEM'95, Lecture Notes in Comp. Science, Vol. 1012, Springer, 1995, pp. 449 - 454.
  • Rozloznik, M. and Strakos, Z. Variants of the Residual Minimizing Krylov Space Methods, In: Proceedings of the XI. Summer School Software and Algorithms of Numerical Mathematics, I.Marek et al. (eds), Plzen, U. of West Bohemia, 1996, pp. 208 - 225.
  • Greenbaum, A. and Strakos, Z. Matrices that Generate the Same Krylov Varieties, in: Recent Advances in Iterative Methods, G.H.Golub et al. (eds.), IMA Volumes in Maths and Its Applications, Springer 1994, pp. 95-119.
  • Strakos, Z. and Tuma, M. Current Trends in Numerical Linear Algebra: From Theory to Practice, Proceedings of the SOFSEM'94, M. Bartosek (ed.), Brno, Czech Soc. of Comp. Science, 1994, pp.229 -249.
  • Strakos, Z. Lanczos Algorithm, Orthogonal Polynomials and Continued Fractions, Proceedings of the X. Summer School Software and Algoriths of Numerical Mathematics, I. Marek et al. (eds.), Prague, Charles University 1993, pp. 179-186.
  • Strakos, Z. and Greenbaum, A. Open Questions in the Convergence Analysis of the Lanczos Process For the Real Symmetric Eigenvalue Problem, IMA Research Rep. 934, March 1992.
  • Strakos, Z. A Note on the Rate of Convergence of the Conjugate Gradient method and the Convergence of Ritz Values, Proceedings NATO ASI on Computer Algorithms for Solving Linear Equations: the State of the Art (Contributed Papers), Il Ciocco, Sept. 1990, pp. 100-117.
  • Strakos, Z. Large Scale Numerical Computations Using Peripheral Array Processors, Proceedings Algorithms'89, Strbske Pleso, April 1989, pp. 300-303.
  • Strakos, Z. On the Rate of Convergence of the Conjugate Gradient Method for Solution of Linear Systems, Proceedings ECS'87, Praha 1987, pp.184-189.
  • The list above is extracted from a complete list of 85 publications.