Answer: Use the method of Steepest Descent to approximate minima to within 0.005 for the

Chapter 10, Problem 5

(choose chapter or problem)

Use the method of Steepest Descent to approximate minima to within 0.005 for the following functions.

a. \(g\left(x_{1}, x_{2}\right)=\cos \left(x_{1}+x_{2}\right)+\sin x_{1}+\cos x_{2}\)

b. \(g\left(x_{1}, x_{2}\right)=100\left(x_{1}^{2}-x_{2}\right)^{2}+\left(1-x_{1}\right)^{2}\)

c. \(g\left(x_{1}, x_{2}, x_{3}\right)=x_{1}^{2}+2 x_{2}^{2}+x_{3}^{2}-2 x_{1} x_{2}+2 x_{1}-2.5 x_{2}-x_{3}+2\)

d. \(g\left(x_{1}, x_{2}, x_{3}\right)=x_{1}^{4}+2 x_{2}^{4}+3 x_{3}^{4}+1.01\)