Numerical Methods For Engineers, 7 Ed
7th Edition
ISBN: 9789352602131
Author: Canale Chapra
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Textbook Question
Chapter 14, Problem 8P
Perform one iteration of the optimal gradient steepest descent method to locate the minimum of
using initial guesses
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Your ID's last three digits are "abc". Let f(x,y) = 2x²+y²-xy-6x. Find the minimum of function by applying the Gradient
Descent method twice with the initial point (1,1). First iteration stepsize is m=(1+a+b+c)/10 and the second iteration stepsize
is 0.1. Use two decimals in your calculations.
Update: +1 = Xi
Yi+1=Yi -
fx (xi, Yi)
|▼ f (xi, Yi)|
fy (xi, Yi)
Vf(xi, Yi)
As
-As
Gradient: Vf (₁, y) = √(x(i, Yi))² + (fy (i, Yi))²
27
a=0,b=3,c=9 please solve that numerical analysis question on that information.
Chapter 14 Solutions
Numerical Methods For Engineers, 7 Ed
Ch. 14 - 14.1 Find the directional derivative of
at in...Ch. 14 - Repeat Example 14.2 for the following function at...Ch. 14 - 14.3 Given
Construct and solve a system of...Ch. 14 - (a) Start with an initial guess of x=1 and y=1 and...Ch. 14 - 14.5 Find the gradient vector and Hessian matrix...Ch. 14 - Prob. 6PCh. 14 - Perform one iteration of the steepest ascent...Ch. 14 - Perform one iteration of the optimal gradient...Ch. 14 - Develop a program using a programming or macro...Ch. 14 - 14.10 The grid search is another brute force...
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