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

Mohammed Yusuf Waziri | Zendy; Zanariah Abdul Majid | Zendy

Open Access

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

Author(s) -

Mohammed Yusuf Waziri,

Zanariah Abdul Majid

Publication year - 2013

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2013/875935

Subject(s) - jacobian matrix and determinant , diagonal , mathematics , nonlinear system , cauchy distribution , quasi newton method , initial value problem , scale (ratio) , mathematical analysis , newton's method , geometry , physics , quantum mechanics

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

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