Displaying similar documents to “Convergence of extrapolation coefficients”

Improving the convergence of iterative methods

Jan Zítko (1983)

Aplikace matematiky

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The author considers the operator equation x = T x + b . Methods for acceleration of convergence of the iterative process x n + 1 ) = T x n + b are investigated.

A unified convergence theory for L ⁢ R and Q ⁢ R algorithms applied to symmetric eigenvalue problems

R. I. Peluso, G. Piazza (2002)

Bollettino dell'Unione Matematica Italiana

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In this paper we consider the eigenvalue problem for positive definite symmetric matrices. Convergence properties for the zero shift Q ⁢ R method and the shift L ⁢ R Cholesky method both in restoring and in non restoring version are deduced from the convergence properties of triangular matrices sequences. For general matrices we obtain some results on the convergence speed of the Cholesky method as a function of the chosen shift. These results follow from the absolute convergence of numerical...

Combining the preconditioned conjugate gradient method and a matrix iterative method

Jan Zítko (1996)

Applications of Mathematics

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The preconditioned conjugate gradient method for solving the system of linear algebraic equations with a positive definite matrix is investigated. The initial approximation for conjugate gradient is constructed as a result of a matrix iteration method after m steps. The behaviour of the error vector for such a combined method is studied and special numerical tests and conclusions are made.