Code Provided In eLearning %find root of f(x) = 0 %using Bisection Method format

Question

Code Provided In eLearning

%find root of f(x) = 0
%using Bisection Method

format long e

%chosen error tolerance (TOL)
TOL = .000001;

%choose max number of iterations
MAXIT = 50;

%initial bracket
a = ;
b = ;

%keep track of number of iterations
count = 0;

%record iterates - a col vector of MAXIT length
cits = zeros(MAXIT,1);

%evaluate func. at a and b
fa = fbisect(a);
fb = fbisect(b);

%stop if not appropriate interval
if sign(fa)*sign(fb) >= 0
  
return
  
end

%stop loop when error less than TOL or MAXIT reached
while abs(b-a)/2 >= TOL & count < MAXIT

%get midpoint(root estimate)
c = (a + b)/2;
  
%eval. func at midpoint
fc = fbisect(c);
  
%stop if f(c)=0
if fc == 0
break
end
  
%update count
count = count + 1;
  
%add to list of iterates
cits(count) = c;

%if sign change between a and c make c the new right endpt
if sign(fa)*sign(fc)<0   
  
b = c;
  
%if sign chg betw c and b make c the new left endpt   
else

a = c;
  
end
  
end

%update count
count = count + 1;

%get final midpoint(root estimate)
c = (a+b)/2;
  
%add to vector of iterates
cits(count) = c;
  
%display error estimate
error = abs(b-a)/2

%display vector of iterates
cits

%display number of iterates
count   

1) Modify the code bisect.m (provided in eLeaning) to write a new script, falposm that performs the Method of False Position. You will only need to add/modify a few lines of code. Run your script to compute approximations to the xcoordinates of any intersections of the ellipse (x-2 -(y-1). 1 and the parabola y=(x-2),1. For each intersection, you will need to 4 determine an initial bracket to use in your script (a sketch of the graphs would be helpful here) Also, write a separate function m-file, falpos.m to compute an appropriate function whose roots you will need to approximate for the xcoordinates of the intersections

Explanation / Answer

function [x,iter] = regulaFalsi(f,a,b,e)
error=1;
wlast=1;
iter=0;
while error>e
w=(a*subs(f,b)-b*subs(f,a))/(subs(f,b)-subs(f,a));
w=double(vpa(w));
[a w b]
if double(vpa(subs(f,w)))*double(vpa(subs(f,w)))>0
a=w;
else
b=w;
end
error=abs(wlast-w);
wlast=w;
iter=iter+1;
%[iter error]
pause
end
x=wlast;
end

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