FminDemo.m

Contents

Overview

Illustrates the NCM routine fmintx (textbook version of fminbnd) to find a local minimum of $f$ on the interval $[x_0, x_1]$.

First Example: Find a local minimum of the Bessel function $J_0$

We use the interval $[x_0,x_1] = [0,30]$

disp('Find a local minimum of the Bessel function J0:')
J0 = @(x) besselj(0,x);
disp('Interval is [a,b] = [0,30]')
fmintx(J0,0,30);
x = fmintx(J0,0,30);
disp(sprintf('A local minimum of J0 is %f attained at x = %f.\n',J0(x),x))
x = [0:.1:30];
plot(x, besselj(0,x))

Find a local minimum of the Bessel function J0:
Interval is [a,b] = [0,30]
A local minimum of J0 is -0.249705 attained at x = 10.173468.

Second Example: Find the absolute minimum of the Bessel function $J_0$

The previous example demonstrated that fzerotx (or fminbnd) may not be able to find the global minimum. We use therefore need to use a tighter interval. We pick $[x_0,x_1] = [0,10]$.

%pause
disp('To find the absolute minimum of the Bessel function J0')
J0 = @(x) besselj(0,x);
disp('we need to adjust the interval to [a,b] = [0,10]')
x = fmintx(J0,0,10);
disp(sprintf('The minimum of J0 is %f attained at x = %f.\n',J0(x),x))

To find the absolute minimum of the Bessel function J0
we need to adjust the interval to [a,b] = [0,10]
The minimum of J0 is -0.402759 attained at x = 3.831706.

Second Example: Find the minimum of the function $f(x) = x^2-2$

We use the interval $[x_0,x_1] = [-2,2]$

%pause
disp('Compute the minimum of f(x)=x^2-2:')
sqr2 = @(x) x.^2-2;
disp('Interval is [a,b] = [-2,2]')
x = fmintx(sqr2,-2,2);
disp(sprintf('Minimum of f is %f attained at x=%f.',sqr2(x),x))
x = [-2:.1:2];
plot(x, sqr2(x))

Compute the minimum of f(x)=x^2-2:
Interval is [a,b] = [-2,2]
Minimum of f is -2.000000 attained at x=-0.000000.


© Greg Fasshauer, IIT. Published with MATLAB® 7.11