Secant methods for semismooth equations |
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| Authors: | Florian A Potra Liqun Qi Defeng Sun |
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| Institution: | (1) Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA; e-mail: potra@math.uiowa.edu , US;(2) School of Mathematics, The University of New South Wales, Sydney, New South Wales 2052, Australia; e-mail: (Liqun Qi) L.Qi@unsw.edu.au, (Defeng Sun) sun@alpha.maths.unsw.edu.au , AU |
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| Abstract: | Some generalizations of the secant method to semismooth equations are presented. In the one-dimensional case the superlinear
convergence of the classical secant method for general semismooth equations is proved. Moreover a new quadratically convergent
method is proposed that requires two function values per iteration. For the n-dimensional cases, we discuss secant methods for two classes of composite semismooth equations. Most often studied semismooth
equations are of such form.
Received October 16, 1996 / Revised version received July 25, 1997 |
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