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- Anne Greenbaum, Vlastimil Pták, Zdenek Strakos
- SIAM J. Matrix Analysis Applications
- 1996

Given a nonincreasing positive sequence, f(0) f(1) : : : f(n ? 1) > 0, it is shown that there exists an n by n matrix A and a vector r 0 with kr 0 k = f(0) such that f(k) = kr k k, k = 1; : : :; n ? 1, where r k is the residual at step k of the GMRES algorithm applied to the linear system Ax = b, with initial residual r 0 = b?Ax 0. Moreover, the matrix A… (More)

- Marián Fabian, Petr Hájek, Vicente Montesinos, V. Zizler, Vlastimil Pták
- 2005

A quantitative version of Krein’s Theorem on convex hulls of weak compact sets is proved. Some applications to weakly compactly generated Banach spaces are given.

- Vlastimil Pták
- Discrete Mathematics
- 1992

— An aiiempt to set up a method for estimating convergence of itérative processes using inequalities of the type where (Ù is a "small" fonction as deflned by the author. This method is compared with the classical notion of a rate of convergence ; for convex fonctions (ù inequalities using the distance of xn from the solution and those using the distance of… (More)

- Vlastimil Pták
- Discrete Mathematics
- 2001

- Antonín Leanovsky, Vlastimil Pták
- Discrete Mathematics
- 1986

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