A Shamanskii-Like Accelerated Scheme for Nonlinear Systems of Equations

Mohammed, Dr. Ibrahim Sulaiman and Mamat, Prof. Dr. Mustafa (2020) A Shamanskii-Like Accelerated Scheme for Nonlinear Systems of Equations. In: Nonlinear Systems: Theoretical Aspects and Recent Applications. IntechOpen, United Kingdom, pp. 1-12. ISBN 978-1-78985-472-5

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Abstract

Newton-type methods with diagonal update to the Jacobian matrix are regarded 09 as one most efficient and low memory scheme for system of nonlinear equations. 10 One of the main advantages of these methods is solving nonlinear system of equa11 tions having singular Fréchet derivative at the root. In this chapter, we present a 12 Jacobian approximation to the Shamanskii method, to obtain a convergent and 13 accelerated scheme for systems of nonlinear equations. Precisely, we will focus on 14 the efficiency of our proposed method and compare the performance with other 15 existing methods. Numerical examples illustrate the efficiency and the theoretical 16 analysis of the proposed methods.

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