I have a question to solve and i really don't know how. if someone can help me please??????
Maria
The "method of steepest descent" is a numerical method. To find a minimum for f(x,y), starting at $\displaystyle (x_0, y_0)$, find the direction of $\displaystyle -\nabla f(x_0,y_0)$ and move a short distance in that direction. Repeat until $\displaystyle \nabla f(x_0, y_0)$ is short enough.
For this problem, $\displaystyle \nabla (x^2+ 1.1y^2)= 2x\vec{i}+ 2.2y\vec{j}$ and at (6, 3), that is $\displaystyle 12\vec{i}+ 6.6\vec{j}$. Just to make it "small" let's multiply that by, say, .1 to get $\displaystyle 1.2\vec{i}+ .22\vec{j}$. We want to move from (6, 3) in the opposite direction from that so subtract (1.2, .22) from (6, 3) to get (4.8, 2.78). Now repeat. Find $\displaystyle \nabla f$ at that point and subtract.
can you please tell me if my results are correct?
I found a=0.488 and x1=[0.144;-0.2208], a=0.466 and x2=[0.00979;0.00556]
, and a=0.4863 x3=[0.000268;-0.000388] can youi please just check theses results cause i am not sure. and i stop here i don't know if i must go on and do it again. Thank you