The effects of finite-difference approximation of derivatives on Newton's method

Date

5-1992

Degree

Bachelor of Science in Agriculture

College

College of Arts and Sciences (CAS)

Adviser/Committee Chair

Norberto R. Navarrete Jr.

Abstract

This paper studies the effects of using finite-difference approximation of derivatives on the classical Newton's method for unconstrained minimization problem. The exact-Newton (Newton's method which uses analytic form of the derivatives) is compared with the discrete-Newton (Newton's method which uses finite-difference approximation of derivatives). The exact- and discrete-Newton methods are practically the same in performance in solving the majority of the test problems in order to reach convergence. As expected, due to the multiple function evaluations in approximating the gradients and the hessians, the discrete-Newton is less satisfactory in terms of computational speed than the exact-Newton. In the cases where the number of iterations are practically the same for both methods, the overall CPU time of the discrete-Newton method is found to be 4 to 12 times longer than the exact-Newton. While the total CPU time needed to evaluate the derivatives in the discrete-Newton method is found to be 2 to 8 times longer than that in the exact-Newton.

Language

English

Location

UPLB Main Library Special Collections Section (USCS)

Call Number

Thesis

Document Type

Thesis

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