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National Repository of Grey Literature 4 records found  Search took 0.00 seconds. 
Approaches to analysis of Krylov subspace methods
 Outrata, Michal ; Strakoš, Zdeněk (advisor) ; Knobloch, Petr (referee)
The text deals with the understanding of the convergence behaviour of the GMRES method. The first part reviews results formulated for the linear algebraic finite-dimensional problem Ax = b. The second part revisits the question on whether the algebraic GMRES behaviour can be analyzed using bounded operators on an infinite-dimensional Hilbert spaces. 1
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Teoretické otázky popisu chování krylovovských metod
 Strnad, Otto ; Strakoš, Zdeněk (advisor) ; Zítko, Jan (referee)
The presented thesis is focused on the GMRES convergence analysis. The basic principles of CG, MINRES and GMRES are briefly explained. The thesis summarizes some known convergence results of these methods. The known characterizations of the matrices and the right hand sides gen- erating the same Krylov residual spaces are summarized. Connections and the differences between the different points of view on GMRES convergence analysis are shown. We expect that if the convergence curve of GMRES applied to the nonnormal matrix and the right hand side seems to be de- termined by the eigenvalues of the matrix then exists a matrix that is close to normal and has the same spectrum as the matrix and for the right hand side has the same GMRES convergence curve (We assume that the initial approximation 0 = 0). Several numerical experiments are done to examine this assumption. This thesis describes an unpublished result of Gérard Meu- rant which is the formula for the norm of the -th error of GMRES applied to the matrix and right hand side and its derivation. The upper estimate of the -th GMRES error is derived. This estimate is minimized via spectrum.
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Worst-case GMRES pro normální matice
 Liesen, J. ; Tichý, Petr
We study the convergence of GMRES for linear algebraic systems with normal matrices. In particular, we explore the standard bound based on a min-max approximation problem on the discrete set of the matrix eigenvalues.
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Residuals and Singular Values in Linear Least Squares Problems
 Paige, Ch. ; Strakoš, Zdeněk
Fulltext: content.csg - Download fulltextPDF
Plný tet: v765-98 - Download fulltextPDF
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