An Improved Diagonal Jacobian Approximation via a New Quasi‐Cauchy Condition for Solving Large‐Scale Systems of Nonlinear Equations

Mohammed Yusuf Waziri and Zanariah Abdul Majid

Journal of Applied Mathematics, 2013, vol. 2013, issue 1

Abstract: We present a new diagonal quasi‐Newton update with an improved diagonal Jacobian approximation for solving large‐scale systems of nonlinear equations. In this approach, the Jacobian approximation is derived based on the quasi‐Cauchy condition. The anticipation has been to further improve the performance of diagonal updating, by modifying the quasi‐Cauchy relation so as to carry some additional information from the functions. The effectiveness of our proposed scheme is appraised through numerical comparison with some well‐known Newton‐like methods.

Date: 2013
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https://doi.org/10.1155/2013/875935

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2013:y:2013:i:1:n:875935

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