Question

Consider the function f(x) = x3 – 2x2 + x Write the MATLAB code in the format of "script file" using "Regula Falsi Method" with the estimated relative error of 0.000001 and upload the script file. Direction: 1) Please submit"script file", NOT "function file". If you submit a function file, I will assign ZERO score. 2) You can find some matlab code for the Regula Falsi Method on a web or some books. You can use any code you can find but when you write the code, you should write "comment" which explains the code. Clearly, when you use the code, you need to modify the code tailored to the above question. Upload Choocan Gila

Answer 1

clc;

clear all ;

%regula falsi method

f = @(x) (x^3-2*x^2+1.5*x); % the given function

n=0.1;

while (f(n)*f(-n) > 0) % here we are finding the the interval [a,b] where the f(a)f(b)<0

n=n+0.1;

end

a=-n; % f has a root in [a,b]

b=n;

%%%% here we are calculating the 1st approximation of the root c(1)

c(1)=(a*f(b)-b*f(a))./(f(b)-f(a)); % here we are using the Regula-Falsi method, c=(a*f(b)-b*f(a))/(f(b)-f(a))

if f(a)*f(c(1))<0 % if f (a) * f (c) < 0 then b = c else a = c

b=c(1);

else

a=c(1);

end

error=10;

i=2;

while (error>0.000001)

c(i)=(a*f(b)-b*f(a))./(f(b)-f(a)); % here we are using the Regula-Falsi method, c=(a*f(b)-b*f(a))/(f(b)-f(a))

if f(a)*f(c(i))<0 % if f (a) * f (c) < 0 then b = c else a = c

b=c(i);

else

a=c(i);

end

error=abs(abs(c(i)-c(i-1))./c(i)); % calculating relative error

i=i+1;

end

fprintf('The root with the relative error of 0.000001 is %f',c(end))

regula_falsi.mx + clc; clear all ; %regula falsi method f = @(x) (x^3-2*x^2+1.5*x); % the given function n=0.1; while (f(n)*f(-n) > 0) % here we are finding the the interval [a,b] where the f(a) f(b)<o n=n+0.1; end a=-n; % f has a root in [a, b] b=n; %%%% here we are calculating the 1st approximation of the root c(1) c(1)=(a*f(b)-b*f(a))./(f(b)-f(a)); % here we are using the Regula-Falsi method, C=(a*f(b)-b*f(a))/(f(b)-f(a)) if f(a) f(c(1))< % if f (a) * f (c) < then b = c else a = C b=C(1); else a=c(1); end error=10; TL LLL LLL LLL LLL i=2; while (error>0.000001) C(i)=(a*f(b)-b*f(a))./(f(b)-f(a)); % here we are using the Regula-Falsi method, C=(a*f(b)-b*f(a))/(f(b)-f(a)) if f(a) f(c(i) < % if f (a) * f (c) < then b = c else a = c b=c(i); else a=c(i); end error=abs(abs(c(i)--(i-1))./c(i)); % calculating relative error i=i+1; end fprintf('The root with the relative error of 0.000001 is %f",c(end))

COMMAND WINDOW The root with the relative error of 0.000001 is 0.000000 >>