Question

Numerical method. im more interested in point c.

EE2E11-1 1. We require to find the values of (,y), which minimise the following function )12242.5-45ry+82-12+25 (a) Describe briefly the method of gradient descent for minimising functions 5 marks) (b) Assuming that the current estimate of the solution is n, the following update equations are used to minimise f(,y) wrt r,y. af Calculate an optimal value for h if the current estimate is (ro,30)-(0,0) 10 marks (c) Write a Matlab snippet that implements 5 iterations of these updates, returns the required derivatives, di = and d2 at (zu) using the 10 marks] starting from (ro, to)-(0,0)DYou may assume that the function slope (x , y) Matlab invocation [d1,d2] slope(x,y)

Answer 1

Answer:

The MATLAB snippet is as follows, and assumes that the slope function, which returns the required derivatives, is given:

CODE:

%% Inputs

x_0 = 0; % current estimate for x-coordinate

y_0 = 0; % current estimate for y-coordinate

x = [x_0]; % array which will hold all x-estimates

y = [y_0]; % array which will hold all y-estimates

h = 0.01; % arbitrary step value assumed

%% Gradient Descent Snippet

for i = 1:5 % Loop for doing 5 iterations

    [d1, d2] = slope(x(i),y(i)); %calculate derivatives required

    x_temp = x(i) - h*d1; % perform gradient step in x-direction

    y_temp = y(i) - h*d2; % perform gradient step in y-direction

    x = [x x_temp]; % update array holding x-estimates

    y = [y y_temp]; % update array holding y-estimates

end