Publications in Journals

E. C. Carson, J. Liesen and Z. Strakos, Towards understanding CG and GMRES through examples, Linear Algebra and its Applications, 692, 2024, pp. 241-291. . [download]

B. F. Nielsen and Z. Strakos, A simple formula for the generalized spectrum of second order self-adjoint differential operators, SIAM Review, 66, 2024, pp. 125-146. Copyright C by SIAM. Unauthorized reproduction of this article is prohibited. [download]

T. Gergelits, B. F. Nielsen and Z. Strakos, Numerical approximation of the spectrum of self-adjoint operators in operator preconditioning, Numerical Algorithms, Published online June 1, 2022. The Version of Record is available online at: http://dx.doi.org/10.1007/s11075-022-01263-5. Use of this Accepted Version is subject to the publisher Accepted Manuscript terms of use https://www.springernature.com/gp/open-research/policies/acceptedmanuscript-terms. [download]

T. Gergelits, B. F. Nielsen and Z. Strakos, Generalized spectrum of second order differential operators, SIAM Journal on Numerical Analysis, 58, 2020, pp. 2193-2211, also accessible via arxiv. [download] [download]

E. Carson and Z. Strakos, On the Cost of Iterative Computations, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 378, 2020, http://dx.doi.org/10.1098/rsta.2019.0050 (Note: this paper is a follow-on from the invited lecture given by Erin Carson at the Royal Society in April 2019.)

https://royalsocietypublishing.org/doi/10.1098/rsta.2019.0050

J. Hrncir, I. Pultarova and Z.Strakos, Decomposition of subspaces preconditioning: abstract framework, Numerical Algorithms, 83, 2020, pp. 57-98. [download]

T. Gergelits, K.-A. Mardal, B. F. Nielsen and Z. Strakos, Laplacian preconditioning of elliptic PDEs: localization of the eigenvalues of the discretized operator, SIAM Journal on Numerical Analysis, 57, 2019, pp. 1369 - 1394. [download]

S. Pozza and Z. Strakos, Algebraic description of the finite Stieltjes moment problem, Linear Algebra Appl., 561, 2019, pp. 207-227. [download]

S. Pozza, M. Pranic and Z. Strakos, The Lanczos algorithm and complex Gauss quadrature, Electronic Transactions on Numerical Analysis (ETNA), 50, 2018, pp. 1- 19.[download]

E. Carson, M. Rozloznik, Z. Strakos, P. Tichy, and M. Tuma, The numerical stability analysis of pipelined conjugate gradient methods: Historical context and methodology , SIAM. J. Sci. Comput., 40, 2018, A3549 - A3580. [download]

J. Papez and Z. Strakos, On a residual-based a posteriori error estimator for the total error, IMA J. Numer. Anal., 38, 2018, pp. 1164-1184.

J. Papez, Z. Strakos and M. Vohralik, Estimating and localizing the algebraic and total numerical errors using flux reconstructions, Numerische Mathematik, 138, 2018, pp. 681-721.

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. [download]

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.