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Efficient Acceleration Techniques for Fixed Point Algorithms

R. Saigal and M. J. Todd
SIAM Journal on Numerical Analysis
Vol. 15, No. 5 (Oct., 1978), pp. 997-1007
Stable URL: http://www.jstor.org/stable/2156718
Page Count: 11
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Efficient Acceleration Techniques for Fixed Point Algorithms
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Abstract

Recently, Saigal has presented an acceleration technique whereby the fixed point algorithms based on complementary pivoting can be made to converge quadratically. In this paper, we study the efficiency (Brent [1]) of this acceleration, when along with the fixed point steps, a series of Newton type steps are performed. We show that this efficiency is comparable to that of Shamanskii's method and that the "global" convergence properties of the original fixed point algorithm are not destroyed.

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