function pass_fun %J. M. Hill 2011 %Incremental Search Root Finder with Bisection Method with function passed %through argument list xleft = 0.; %input start of interval xright= 4.; %input end of interval a = xleft; %save original for plot range b = xright; %save original for plot range nsteps = 20; %number of steps on the interval epsilon = .0001; %set convergence criterion dx = (xright - xleft)/nsteps; %determine step size x = xleft; %initialize x to left side of the interval while (x <= xright) %use incremental search to step along x axis y = f(x); %evaluate function at left end of intervel x = x + dx; %increment x yright = f(x); %evaluate function on right side of interval if(y * yright <= 0) %a root is trapped in the interval root = findroot(x,dx,y,epsilon); %invoke the bisection method fprintf('root = %6.4f y = %6.4g\n',root,f(root)); end end fn = @f; %get function handle plotxy(a,b,fn); %pass interval limits and function handle to plotxy end %-------------------------------------------------------------------------- function root = findroot(xright,dx,yleft,epsilon) %locate the root in the sub-interval using the bisection technique xleft = xright - dx; %back up to left side of interval while(abs(yleft) >= epsilon) xmid = (xleft + xright)/2.; ymid = f(xmid); if(ymid*yleft < 0.) %root is in the left half of the interval xright = xmid; else %root is in the right half of the interval xleft = xmid; yleft = ymid; end end root = xleft; end %-------------------------------------------------------------------------- function fx = f(x) fx = x*sin(x^2); end %-------------------------------------------------------------------------- function plotxy(a,b,fn) dx = (b - a)/100; xx = a; for i = 1:101 x(i) = xx; y(i) = fn(xx); xx = xx + dx; end plot(x,y) title('Plot of x vs. y') xlabel('x') ylabel('y') grid end
root = 0.0000 y = 0 root = 1.7724 y = 3.217e-005 root = 2.5066 y = -7.49e-005 root = 3.0700 y = 6.253e-005 root = 3.5449 y = -2.728e-005 root = 3.9633 y = 8.521e-006
![](pass_fun_01.png)