The Chebyshev–Shamanskii Method for Solving Systems of Nonlinear Equations

Bilel Kchouk () and Jean-Pierre Dussault ()
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Bilel Kchouk: University of Sherbrooke
Jean-Pierre Dussault: University of Sherbrooke

Journal of Optimization Theory and Applications, 2013, vol. 157, issue 1, No 10, 148-167

Abstract: Abstract We present a method, based on the Chebyshev third-order algorithm and accelerated by a Shamanskii-like process, for solving nonlinear systems of equations. We show that this new method has a quintic convergence order. We will also focus on efficiency of high-order methods and more precisely on our new Chebyshev–Shamanskii method. We also identify the optimal use of the same Jacobian in the Shamanskii process applied to the Chebyshev method. Some numerical illustrations will confirm our theoretical analysis.

Keywords: Newton method; Chebyshev method; Shamanskii process; Algorithm efficiency; Automatic differentiation (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10957-012-0159-6

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