Roots of Equations - Numerical Methods in Engineering with MATLAB - page 147

for n , we get

ln ( | x | /ε )

n = (4.1)

ln2

bisect

Thisfunctionuses the method of bisection to compute the root of f ( x ) 0that is

known to lie in the interval( x1,x2 ). The number of bisections n required to reduce
the intervalto tol iscomputed fromEq. (4.1). The input argument filter controls
the filtering of suspected singularities.Bysetting filter = 1 , weforce the routine
to check whether the magnitudeof f ( x ) decreases with each intervalhalving. If it does
not, the “root” may not be aroot at all, but a singularity, in which case root = NaN is
returned. Since thisfeature is not always desirable, the default value is filter = 0 .

=

function root = bisect(func,x1,x2,filter,tol)
%Findsabracketedzerooff(x)bybisection.
% USAGE: root = bisect(func,x1,x2,filter,tol)
% INPUT:
% func = handle of function that returns f(x).
% x1,x2 = limits on interval containing the root.
%filter=singularityfilter:0=off(default),1=on.
% tol = error tolerance (default is 1.0e4*eps).

% OUTPUT:
% root = zero of f(x), or NaN if singularity suspected.

if nargin < 5; tol = 1.0e4*eps; end
if nargin < 4; filter = 0; end
f1 = feval(func,x1);
if f1 == 0.0; root = x1; return; end
f2 = feval(func,x2);
if f2 == 0.0; root = x2; return; end
if f1*f2 > 0;
error('Root is not bracketed in (x1,x2)')

end
n = ceil(log(abs(x2 - x1)/tol)/log(2.0));
fori=1:n
x3 = 0.5*(x1 + x2);
f3 = feval(func,x3);
if(filter == 1) & (abs(f3) > abs(f1))...
& (abs(f3) > abs(f2))