8. Let f(x, y) be a cost function with two parameters: x and y, and f(x, y) = y³x²y² + y + 3. For the following questions, give your answers to two decimal places. (a) Report the function value for the given initial values of x and y. The initial values are xold = 1, yold = 0. (b) Perform one iteration of the gradient descent algorithm. Set the learning rate to € = 0.01. (c) Find the Hessian matrix of f(x, y).
8. Let f(x, y) be a cost function with two parameters: x and y, and f(x, y) = y³x²y² + y + 3. For the following questions, give your answers to two decimal places. (a) Report the function value for the given initial values of x and y. The initial values are xold = 1, yold = 0. (b) Perform one iteration of the gradient descent algorithm. Set the learning rate to € = 0.01. (c) Find the Hessian matrix of f(x, y).
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:8.
Let f(x, y) be a cost function with two parameters: x and y, and
f(x, y) = y³x²y² + y + 3. For the following questions, give your answers to two decimal places.
(a) Report the function value for the given initial values of x and y. The initial values are
xold = 1, yold = 0.
(b) Perform one iteration of the gradient descent algorithm. Set the learning rate to € = 0.01.
(c) Find the Hessian matrix of f(x, y).
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