 # Numerical Analysis Problem

## Question Show transcribed text

## Transcribed Text

Problem 1. Consider the following unconstrained minimization problem = - - xER³ Suppose we would like to use the steepest descent method to solve it with initial point x(0) = (0,2,1)T. . (b) Write a program to compute the sequence x (k) with the stopping criterion Il V f(xe(t))12_<10-6 . Check whether x (1) is the same as your result in (a). Find the last x(k) in the sequence. Compute each Il Vf(xx(k) ||2 and plot them in a figure. Note that it should be descreasing curve.

## Solution Preview

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ff = @(x1,x2,x3) (2*x1-x2+x3)^2+(x2-1)^2+4*(x3+1)^2;
f = @(x) ff(x(1),x(2),x(3));

gg = @(x1,x2,x3) [4 *(2*x1 - x2 + x3); 2*(-1 + x2) - 2*(2*x1 - x2 + x3); 8*(1 + x3) + 2* (2* x1 - x2 + x3)];
g = @(x) gg(x(1),x(2),x(3));

x0 = [0; 2; 1];

eps = 1e-6;
ngx = eps + 1;

xx = x0; ngrad...
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