Newton’s Method for One-Dimensional Optimization. Major: All Engineering Majors Authors: Autar Kaw, Ali Yalcin http://nm.mathforcollege.com Transforming Numerical Methods Education for STEM Undergraduates. Newton’s Method http://nm.mathforcollege.com. Newton’s Method-Overview.
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Newton’s Method for One-Dimensional Optimization
Major: All Engineering Majors
Authors: Autar Kaw, Ali Yalcin
Transforming Numerical Methods Education for STEM Undergraduates
Initialization: Determine a reasonably good estimate for the maxima or the minima of the function .
Step 1. Determine and .
Step 2. Substitute (initial estimate for the first iteration) and into
to determine and the function value in iteration i.
Step 3.If the value of the first derivative of the function is zero then you have reached the optimum (maxima or minima). Otherwise, repeat Step 2 with the new value of
The cross-sectional area A of a gutter with equal base and edge length of 2 is given by
Find the angle which maximizes the cross-sectional area of the gutter.
The function to be maximized is
Iteration 1: Use as the initial estimate of the solution
Summary of iterations
Remember that the actual solution to the problem is at 60 degrees or 1.0472 radians.
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