Keywords:
- A posteriori error analysis
- Adaptivity
- Algebraic error
- core problem
- delay of convergence
- Discretization error
- exascale computations.
- finite element method
- generalized Jacobi matrices.
- GMRES convergence
- Golub–Kahan bidiagonalization
- inexact computations
- Krylov residual subspace
- Krylov subspace methods
- maximal attainable accuracy
- multiple right-hand sides
- normal matrices
- Numerical solution of partial differential equations
- numerical stability
- pipelined Krylov subspace methods
- Schur parameters
- Spatial distribution of the error
- the conjugate gradient method
- total least squares problem
- unitary matrices
- unitary spectra
Publications of Strakoš, Zdeněk
2020
2019
Algebraic description of the finite Stieltjes moment problem (2019), in: Linear Algebra and its Applications, 561(207-227) | and ,
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2018
Decomposition into subspaces preconditioning: abstract framework (2018), in: SIAM | , and ,
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The Lanczos algorithm and complex Gauss quadrature (2018), in: ETNA (ACTA17 Proceedings), 50(1-19) | , and ,
[DOI] |
The Numerical Stability Analysis of Pipelined Conjugate Gradient Methods: Historical Context and Methodology (2018), in: SIAM J. Sci. Comput., 40:5(A3549–A3580) | , , , and ,
[DOI] [URL] |
2017
Estimating and localizing the algebraic and total numerical errors using flux reconstructions (2017), in: Numerische Mathematik(1-41) | , and ,
[DOI] [URL] |
Gauss quadrature for quasidefinite linear functionals (2017), in: IMA J. Numer. Anal., 37(1468-1495) | , and ,
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LANCZOS ALGORITHM AND THE COMPLEX GAUSS QUADRATURE (2017), in: SIAM Journal on Matrix Analysis and Applications (SIMAX) | , and ,
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2015
Band generalization of the Golub--Kahan bidiagonalization, generalized Jacobi matrices, and the core problem (2015), in: SIAM Journal on Matrix Analysis and Applications, 36:2(417–434) | , and ,
[DOI] |
Band generalization of the Golub-Kahan bidiagonalization, generalized Jacobi matrices, and the core problem (2015), in: SIAM Journal on Matrix Analysis and Applications, 36:2(417-434) | , and ,
[DOI] [URL] |
Preconditioning and the Conjugate Gradient Method in the Context of Solving PDEs, SIAM, SIAM Spotlight Series, 2015 | and ,
[URL] |
2014
Composite convergence bounds based on Chebyshev polynomials and finite precision conjugate gradient computations (2014), in: Numerical Algoritms, 65:4(759-782) | and ,
[DOI] |
Distribution of the discretization and algebraic error in numerical solution of partial differential equations (2014), in: Linear Algebra and its Applications, 449(89–114) | , and ,
[DOI] |
On investigating GMRES convergence using unitary matrices (2014), in: Linear Algebra and its Applications, 450:1(83-107) | , , and ,
[DOI] |
2013
Interplay between discretization and algebraic computation in adaptive numerical solution of elliptic PDE problems (2013), in: GAMM Mitteilungen, 36:1(102-129) | , , and ,
[DOI] |
The Core Problem Within a Linear Approximation Problem Ax ≈ B With Multiple Right-Hand Sides (2013), in: SIAM Journal on Matrix Analysis and Applications, 34:3(917-931) | , and ,
[DOI] |
2012
Analysis of Methods for Matrix Computations: Basic Methods, Matfyzpress, 2012 | , , , and ,
Challenges in coupling iterative algebraic computations with modeling and discretisation PART I - Basic (mostly algebraic) settings, 2012 | , , and ,
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Krylov Subspace Methods Principles and Analysis, Oxford university press, Numerical Mathematics and Scientific Computation, 2012 | and ,
[DOI] [URL] |