Write a program that implements the dogleg method. Choose Bk to be the exact Hessian. Apply it to solve Rosenbrock’s function. Experiment with the update rule for the trust-region by changing the constants in Algorithm 4.1, or by designing your own rules.

Given  > 0, A, E (0, Â), and n € [0, u):
for k = 0, 1, 2, ..
Obtain pk by (approximately) solving (4.3);
Evaluate Pk from (4.4);
if rhoₖ < 5
Δₖ₊₁= 1/4 Δₖ
else
if rhoₖ > 3/4 and || rhox || = Δₖ
Δₖ₊₁ = min(2Δₖ, Â)
else
Δₖ₊₁ = Δₖ;
if rhoₖ > n
Xₖ₊₁ = Xₖ + rhoₖ
else
Xₖ₊₁ = Xₖ;
end (for).

When early motion pictures played in movie theaters, they were often accompanied by live organ or piano music. which of the following are the most likely reasons that this happened? (select all that apply). the music was provided to distract audience members from the loud sounds made when filmstrips were changed. the music accompanied the movies because the movies were silent and audiences were used to hearing music during plays in theaters. the music usually was played before, and sometimes after the movie, as an alternative form of entertainment. the music viewers to interpret the dramatic action in the films.