Consider the function: ƒ(x, y) = x² + 8xy + 4y². (a) Write down two iterations of the gradient descent method for finding the minimum value of the function. Use (1, 1) as the initial point and λ = 0.5. (b) Write down two iterations of the steepest descent method for finding the minimum value of the function. Use (1, 1) as the initial point.
Consider the function: ƒ(x, y) = x² + 8xy + 4y². (a) Write down two iterations of the gradient descent method for finding the minimum value of the function. Use (1, 1) as the initial point and λ = 0.5. (b) Write down two iterations of the steepest descent method for finding the minimum value of the function. Use (1, 1) as the initial point.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Consider the function: f(x, y) = x² + 8xy + 4y².
(a) Write down two iterations of the gradient descent method for finding the
minimum value of the function. Use (1, 1) as the initial point and λ = 0.5.
(b) Write down two iterations of the steepest descent method for finding the
minimum value of the function. Use (1,1) as the initial point.
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