Displaying similar documents to “The effect of rounding errors on a certain class of iterative methods”

On the structure of sets with small doubling property on the plane (I)

Yonutz Stanchescu (1998)

Acta Arithmetica

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Let K be a finite set of lattice points in a plane. We prove that if |K| is sufficiently large and |K+K| < (4 - 2/s)|K| - (2s-1), then there exist s - 1 parallel lines which cover K. We also obtain some more precise structure theorems for the cases s = 3 and s = 4.

A conjugate gradient method with quasi-Newton approximation

Jonas Koko (2000)

Applicationes Mathematicae

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The conjugate gradient method of Liu and Storey is an efficient minimization algorithm which uses second derivatives information, without saving matrices, by finite difference approximation. It is shown that the finite difference scheme can be removed by using a quasi-Newton approximation for computing a search direction, without loss of convergence. A conjugate gradient method based on BFGS approximation is proposed and compared with existing methods of the same class.