Improved Newton's method without direct function evaluations

Authors:
E. N. Malihoutsaki;I. A. Nikas;T. N. Grapsa
Affiliations:
Division of Computational Mathematics and Informatics, Department of Mathematics, University of Patras, GR-26504 Patras, Greece;Division of Computational Mathematics and Informatics, Department of Mathematics, University of Patras, GR-26504 Patras, Greece;Division of Computational Mathematics and Informatics, Department of Mathematics, University of Patras, GR-26504 Patras, Greece
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

For solving systems of nonlinear equations, we have recently developed a Newton's method to manage issues with inaccurate function values or problems with high computational cost. In this work we introduce a modification of the above method, reducing the total computational cost and improving, in general, its overall performance. Moreover, the proposed version retains the quadratic convergence, the good behavior over singular and ill-conditioned cases of Jacobian matrix, and its capability to be ideal for imprecise function problems. Numerical results demonstrate the efficiency of the new proposed method.