(a) Compute one iteration of the gradient descent algorithm for f(x, y) = (x - 2)² + (y + x)² +2 starting at [1,-1] with a learning rate of 1/2. (b) Run the gradient descent algorithm starting from [1,-1] with learning rate set to 1/10 and a threshold of 0.001. How many iterations does it take for the algorithm to terminate and to what vector [x,y] does the algorithm converge? (c) Is [2,-2] a critical point of f(x, y)? (d) Do you think [2,-2] is a global minimum of f(x, y)? Explain why or why not.

(a) Compute one iteration of the gradient descent algorithm for f(x, y) = (x - 2)² + (y + x)² +2 starting at [1,-1] with a learning rate of 1/2. (b) Run the gradient descent algorithm starting from [1,-1] with learning rate set to 1/10 and a threshold of 0.001. How many iterations does it take for the algorithm to terminate and to what vector [x,y] does the algorithm converge? (c) Is [2,-2] a critical point of f(x, y)? (d) Do you think [2,-2] is a global minimum of f(x, y)? Explain why or why not.

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.4: Hyperbolas

Problem 5ECP: Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.

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