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Find the minimum of the Rosenbrock function
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Chapter 13 Solutions
Numerical Analysis
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MathNumerical Analysis
Find the minimum of the Rosenbrock function f ( x , y ) = 100 ( y − x 2 ) 2 + ( x − 1 ) 2 by (a) Newtons Method and (b) Steepest Descent. Use starting guess (2, 2). After how many steps does the solution stop improving? Explain the difference in accuracy that is achieved.
Find the minimum of the Rosenbrock function f ( x , y ) = 100 ( y − x 2 ) 2 + ( x − 1 ) 2 by (a) Newtons Method and (b) Steepest Descent. Use starting guess (2, 2). After how many steps does the solution stop improving? Explain the difference in accuracy that is achieved.
Solution Summary: The author explains how to find the minimum of the Rosenbrock functions by using Newton's Method.
Numerical Analysis
3rd Edition
ISBN: 9780134696454
Author: Sauer, Tim
Publisher: Pearson,
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Textbook Question
Chapter 13.2, Problem 3CP
Expert Solution & Answer
Ch. 13.1 - Prove that the functions are unimodal on some...Ch. 13.1 - Find the absolute minimum in the given intervals...Ch. 13.1 - Plot the function y=f(x) , and find a length-one...Ch. 13.1 - Apply Successive Parabolic Interpolation to the...Ch. 13.1 - Find the point on the hyperbola y=1/x closest to...Ch. 13.1 - Find the point on the ellipse 4x2+9y2=4 farthest...Ch. 13.1 - Prob. 5CPCh. 13.1 - Prob. 6CPCh. 13.1 - Prob. 7CPCh. 13.1 - Prob. 8CP
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