The document presents a MATLAB function for the Regula Falsi method, which is used to find roots of a function. It checks the signs of function evaluations at the endpoints and iteratively refines the interval until a solution is found within specified tolerances. The function also returns the estimated root and the associated error.

1. regula falsi
function[c,err,ys]=regula(f,a,b,delta,epsilon,N)
f=inline('x.^3-2*x-5');
a=2;
b=3;
delta=0.00;
epsilon=0.001;
N=15;
ya=feval(f,a);
yb=feval(f,b);
if ya*yb>0
disp('note: same sign')
end
for i=1:N
dx=yb*(b-a)/(yb-ya);
c=b-dx;
ac=c-a;
yc=feval(f,c)
if yc==0;
break;
elseif yb*yc>0
b=c;
yb=yc;
else
a=c;
ya=yc;
end
dx=min(abs(dx),ac);
if abs(dx)<delta,break,end
if abs(dx)<epsilon,break,end
end
c;
err=abs((b-a)/2);
yc=feval(f,c);
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Taimoor Gondal