Question

3. (30 pts) (Problem 6.2) Determine the highest real root of f(x) 2x3- 11.7x2 + 17.7x -5 a) Graphically. b) Write a MATLAB program using the fixed-point method to determine the root with xo- Write a MATLAB program using the Newton-Raphson method to determine the root with Xo-3. c) d) Write a MATLAB program using the secant method to determine the root with x-1-3 and Xo- 4. e) Compare the relative errors between these three methods at the third iteration (initial value is the zeroth iteration).

Answer 1

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Save file as fixpt.m

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function [k,p,err,P]=fixpt(g,p0,tol,max1)
P(1)=p0;
for k=2:max1
P(k)=feval(g,P(k-1));
err=abs(P(k)-P(k-1));
relerr=err/(abs(P(k))+eps);
p=P(k);
if(err<tol|(relerr<tol))
break;
end
end
if(k==max1)
disp('Maximum iterations exceeded');
end
P=transpose(P);
  
end

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Executable file

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clc
clear all
close all
f=@(x) (2*x^3-5+17.7*x)/(x*11.7);
[k,p,err,P]=fixpt(f,3,1e-6,100);
disp('Root using fixed point');
P(length(P))

2)

clc
clear all
close all
f=@(x) (2*x^3-5+17.7*x-11.7*x^2);
g=@(x) (3*2*x^2+17.7-11.7*2*x);
x0=3;
e=0.0001;
maxit=100;
x1=x0;
x0=0;
N=0;
err=[];
while 1

if abs((x1-x0))>e
x0=x1;
x1=x0-(f(x0)/g(x0));
N=N+1;

else

break;

end
if(N==maxit)
break;
end

end
root=x1;
iter=N;
disp('So, final approximation is')
disp(root)