help fzero
FZERO Single-variable nonlinear zero finding.
X = FZERO(FUN,X0) tries to find a zero of the function FUN near X0,
if X0 is a scalar. It first finds an interval containing X0 where the
function values of the interval endpoints differ in sign, then searches
that interval for a zero. FUN is a function handle. FUN accepts real
scalar input X and returns a real scalar function value F, evaluated
at X. The value X returned by FZERO is near a point where FUN changes
sign (if FUN is continuous), or NaN if the search fails.
X = FZERO(FUN,X0), where X0 is a vector of length 2, assumes X0 is a
finite interval where the sign of FUN(X0(1)) differs from the sign of
FUN(X0(2)). An error occurs if this is not true. Calling FZERO with a
finite interval guarantees FZERO will return a value near a point where
FUN changes sign.
X = FZERO(FUN,X0), where X0 is a scalar value, uses X0 as a starting
guess. FZERO looks for an interval containing a sign change for FUN and
containing X0. If no such interval is found, NaN is returned.
In this case, the search terminates when the search interval
is expanded until an Inf, NaN, or complex value is found. Note: if
the option FunValCheck is 'on', then an error will occur if an NaN or
complex value is found.
X = FZERO(FUN,X0,OPTIONS) solves the equation with the default optimization
parameters replaced by values in the structure OPTIONS, an argument
created with the OPTIMSET function. See OPTIMSET for details. Used
options are Display, TolX, FunValCheck, OutputFcn, and PlotFcns.
X = FZERO(PROBLEM) finds the zero of a function defined in PROBLEM.
PROBLEM is a structure with the function FUN in PROBLEM.objective,
the start point in PROBLEM.x0, the options structure in PROBLEM.options,
and solver name 'fzero' in PROBLEM.solver.
[X,FVAL]= FZERO(FUN,...) returns the value of the function described
in FUN, at X.
[X,FVAL,EXITFLAG] = FZERO(...) returns an EXITFLAG that describes the
exit condition. Possible values of EXITFLAG and the corresponding exit
conditions are
1 FZERO found a zero X.
-1 Algorithm terminated by output function.
-3 NaN or Inf function value encountered during search for an interval
containing a sign change.
-4 Complex function value encountered during search for an interval
containing a sign change.
-5 FZERO may have converged to a singular point.
-6 FZERO can not detect a change in sign of the function.
[X,FVAL,EXITFLAG,OUTPUT] = FZERO(...) returns a structure OUTPUT
with the number of function evaluations in OUTPUT.funcCount, the
algorithm name in OUTPUT.algorithm, the number of iterations to
find an interval (if needed) in OUTPUT.intervaliterations, the
number of zero-finding iterations in OUTPUT.iterations, and the
exit message in OUTPUT.message.
Examples
FUN can be specified using @:
X = fzero(@sin,3)
returns pi.
X = fzero(@sin,3,optimset('Display','iter'))
returns pi, uses the default tolerance and displays iteration information.
FUN can be an anonymous function:
X = fzero(@(x) sin(3*x),2)
FUN can be a parameterized function. Use an anonymous function to
capture the problem-dependent parameters:
myfun = @(x,c) cos(c*x); % The parameterized function.
c = 2; % The parameter.
X = fzero(@(x) myfun(x,c),0.1)
Limitations
X = fzero(@(x) abs(x)+1, 1)
returns NaN since this function does not change sign anywhere on the
real axis (and does not have a zero as well).
X = fzero(@tan,2)
returns X near 1.5708 because the discontinuity of this function near the
point X gives the appearance (numerically) that the function changes sign at X.
See also ROOTS, FMINBND, FUNCTION_HANDLE.
Documentation for fzero
doc fzero
Other uses of fzero
optim/fzero
Unless, of course, this is just your homework. In which case you would have been directed not to use fzero. But then you would need to be doing the work yourself anyway.
