Q$\_$wc $=$ np$.$array$([[1,0\mathrm{.}3],[0\mathrm{.}3,1]])$; q $=$ np$.$array$([0,0])$; Q$\_$sic $=$ np$.$array$([[1,0\mathrm{.}85],[0\mathrm{.}85,1]])$; q $=$ np$.$array$([0,0])$; Q$\_$ic $=$ np$.$array$([[1,0\mathrm{.}99],[0\mathrm{.}99,1]])$; q $=$ np$.$array$([0,0])$; PartA Consider the quadratic functions f$\_$wc$,$ f$\_$sic and f$\_$ic defined by the quadratic matrices above. For each of these, say whether they are $\backslash$beta $-$smooth and$/$or $\backslash$alpha $-$strongly convex, and if so$,$ compute the value of the condition number, k$=\backslash$beta $/\backslash$alpha for each function. PartB Compute the best fixed step size for gradient descent, and the best parameters for accelerated gradient descent. For each function, plot the error f$($x$\_$t$)$f$($x$)$ as a function of the number of iterations. For each function, plot these on the same plot so you can compare $$ so you should have $3$ plots total. Problem $1$: Gradient Descent and Acceleration In this problem you will explore the impact of ill$-$conditioning on gradient descent, and will then see how acceleration can improve the situation. This accelerated gradient descent as the condition number $($ratio of largest to smallest eigenvalues of the Hessian$)$ increases. This is a "toy" problem, but is still instructive regarding the performance of these two algorithms. You will work with the following simple function:

f$($x$)=1/2$ x$^$ Q x$,$

where Q is a $2$ by $2$ matrix, as defined below.