An Improved Diagonal Jacobian Approximation via a New Quasi-Cauchy Condition for Solving Large-Scale Systems of Nonlinear Equations. (19th February 2013)

• Record Type: Journal Article
• Authors: Waziri, Mohammed Yusuf; Abdul Majid, Zanariah
• Other Names: Öziş Turgut Academic Editor.
• Is Part Of: Journal of applied mathematics. Volume 2013(2013)
• Publication Date: 2013-02-19
• Subjects: Mathematics -- Periodicals; 519.05
• DOI: 10.1155/2013/875935
• Languages: English
• ISSNs: 1110-757X

Abstract

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.