USE FOLLOWING FORM

%change Bisection to False Position

format long e

%chosen error tolerance (TOL)

TOL = .000001;

%choose max number of iterations

MAXIT = 50;

%provide initial bracket; for checking initial bracket beloww%%%%%%%%%%%%%%%

a0 = ;

b0 = ;

%transfer to a and b for the algorithm below

a = a0;

b = b0;

%keep track of number of iterations

count = 0;

%record iterates - a col vector of MAXIT length

cits = zeros(MAXIT,1);

%evaluate abs value of func just as a check below%%%%%%%%%%%%%%%

absfa = abs(ffalpos(a));

absfb = abs(ffalpos(b));

%transfer to fa and fb for the algorithm

fa = ffalpos(a);

fb = ffalpos(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

%get midpoint(root estimate)%%%%%%%%%%%%%%%

c = (a + b)/2;

%eval. func at midpoint

fc = ffalpos(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)

b = c;

fb = fc;

%if sign chg betw c and b make c the new left endpt

else

a = c;

fa = fc;

end

end

%get final midpoint(root estimate)%%%%%%%%%%%%%%%

c = (a+b)/2;

%add to vector of iterates

cits(count) = c;

%update count

count = count + 1;

%display error estimate%%%%%%%%%%%%%%%

error = abs(b-a)/2

%display vector of iterates

cits

%display number of iterates

count

%Place function below

%Write your function as a polynomial in x

%Make sure the coefficient of the highest-degree term is 1

function y=fbisect(x)

y=(x-1).^2+(x.^-1).^2-1;

end

The given script file performs the Bisection Method to estimate a root. Modify this code to perform the Method of False Position. You will only need to modify a few lines of code. Run your script to compute approximations to only the greater of the x coordinates of intersections of the ellipse - (x - 2) +(y-1)2 = 1 and the parabola y=(x - 2) +1. Use the location of the 4 center and the right-most point of the ellipse for the endpoints of your initial bracket (a sketch of the graphs would be helpful here). Also, make sure to change the error measure from =to error measure 16-a (This is because the estimate, c, at each step could be anywhere in the interval (a,b)) Also, below the script, write a separate MATLAB function to compute an appropriate mathematical function whose root you will need to approximate for the x coordinate of the intersection. (The first line of this function will take the same form as a function m-file that would be written in the MATLAB software package.) as