Vlastimil Pták

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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)
— 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)
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