Fzero use

1
Lecture 6 Fzero use
2
Matlab function fzero
X FZERO(FUN,X0), X0 a scalar Attempts to find
a zero of the function FUN near X0. FUN is a
function handle. The value X returned by FZERO
is near a point where FUN changes sign (if FUN
is continuous), or NaN, if the srootfinding search
fails. X FZERO(FUN,X0), X0 a 2-vector.
Assumes that FUN(X0(1)) and FUN(X0(2)) differ in
sign, insuring a root. X FZERO(FUN,X0,OPTIONS).
Solves the equation with default optimization
parameters replaced by values in the string
OPTIONS, an argument created with the OPTIMSET
function.
3
Example of fzero use
gtgt options optimset('disp', 'iter', 'tolx',
1.e-15) gtgt fzero(_at_ftest2,0.1 2,options)
Func-count x f(x)
Procedure 2 0.1 -1.6786
initial 3 0.157698 -1.4715
interpolation 4 0.556708
0.601452 interpolation 5
0.440938 -0.143633 interpolation 6
0.463256 -0.0110609
interpolation 7 0.465084 2.0255e-005
interpolation 8 0.465081
-3.08857e-008 interpolation 9
0.465081 -8.61533e-014 interpolation 10
0.465081 0
interpolation Zero found in the interval 0.1,
2 ans 0.4651 gtgt
4
Inclass4
Modify ftest2.m to find root of e(-x)-x0 by
Brents method starting at x0.2 and x1.5
5
Answer to inclass4
gtgt fzero(_at_ftest2b,0.2 1.5,options)
Func-count x f(x)
Procedure 2 0.2 0.618731
initial 3 0.624325 -0.0887015
interpolation 4 0.571121
-0.0062285 interpolation 5
0.567143 1.13316e-006 interpolation 6
0.567143 -8.15018e-010
interpolation 7 0.567143 -1.11022e-016
interpolation 8 0.567143
-1.11022e-016 interpolation Zero found
in the interval 0.2, 1.5 ans 0.5671
6
Practical use of root finding 1)Estimate
approximate position of roots. Use e.g. plot of
function. 2)Find each root separately using
initial points from plot.