1. We require to find the values of (x, y), (x, y) which min- imise the...

 

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1. We require to find the values of (x, y), (x, y) which min- imise the following function. f(x, y) = −8x + x² + 12y + 4y² − 2xy (3) (a) Write down the pair of simultaneous equations which govern the relationship between and ŷ at the location of the minimum. (b) Hence show that the exact solution is â = -0.67. af əx af [5 marks] (c) We instead attempt to use the method of steepest de- scent to solve this problem. Assuming that the current estimate of the solution is n, Yn, why do the following update equations minimise f(x,y)? Xn+1 = Xn-h- Yn+1 Yn-h- [5 marks] მყ 3.33,9 = (4) [3 marks] (d) Calculate an optimal value for h if the current estimate is (xn, Yn)= (0,0) [7 marks] (e) Hence calculate the new estimate of the solution (x1, y₁) 1. We require to find the values of (x, y), (x, y) which min- imise the following function. f(x, y) = −8x + x² + 12y + 4y² − 2xy (3) (a) Write down the pair of simultaneous equations which govern the relationship between and ŷ at the location of the minimum. (b) Hence show that the exact solution is â = -0.67. af əx af [5 marks] (c) We instead attempt to use the method of steepest de- scent to solve this problem. Assuming that the current estimate of the solution is n, Yn, why do the following update equations minimise f(x,y)? Xn+1 = Xn-h- Yn+1 Yn-h- [5 marks] მყ 3.33,9 = (4) [3 marks] (d) Calculate an optimal value for h if the current estimate is (xn, Yn)= (0,0) [7 marks] (e) Hence calculate the new estimate of the solution (x1, y₁)