Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN: 9780133594140
Author: James Kurose, Keith Ross
Publisher: PEARSON
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NEWTON-RAPHSON METHOD

EXAMPLE 1: Find the root of the function ?(?) = cos (?) using NRM having initial approximation of 1

Input the following codes to your MATLAB edit window and name as    “newton.m”

% Newton-Raphson Algorithm            
 
 syms x
 
 %Input section
 y = input('Enter the given function: ');
 yd = input('Enter the derivative of the given function: 
');
 p0 = input('Enter initial approximation: ');
 n = input('Enter no. of iterations, n: ');
 tol = input('Enter tolerance, tol:  ');
 
 
 i = 1;
 while i <= n
    d=(eval(subs(y,x,p0)))/eval(subs(yd,x,p0));
    p0 = p0 - d; 
    if abs(d) < tol
        if i == 3
            fprintf('\nApproximate solution of %s is xn= 
%11.9f on %drd iterations  \n\n',y, p0, i);
        elseif i == 1
            fprintf('\nApproximate solution of %s is xn= 
%11.9f on %dst iterations  \n\n',y, p0, i);
        elseif i == 2
            fprintf('\nApproximate solution of %s is xn= 
%11.9f on %dnd iterations  \n\n',y, p0, i);
        else
            fprintf('\nApproximate solution of %s is xn= 
%11.9f on %dth iterations  \n\n',y, p0, i);
        end
       break;
    else
       i = i+1;
    end
 end

 

Run the program and enter the following.

Enter the given function:  cos(x)
Enter the derivative of the given function:  -sin(x)
Enter initial approximation:  1
Enter no. of iterations, n:  30
Enter tolerance, tol:   0.0001

Write the output below:

NEWTON-RAPHSON METHOD
EXAMPLE 1: Find the root of the function f(x) = cos(x) using NRM having initial approximation of 1
Input the following codes to your MATLAB edit window and name as 'newton.m"
* Newton-Raphson Algorithm
syms x
Input section
y = input ('Enter the given function: ');
yd = input ('Enter the derivative of the given function:
');
p0 = input ('Enter initial approximation: ');
input ('Enter no. of iterations, n:');
tol = input('Enter tolerance, tol: ');
n =
i = 1;
while i <= n
d= (eval (subs (y,x,p0)))/eval(subs (yd, x, p0));
p0 = p0
if abs (d) < tol
if i == 3
d;
||
fprintf('\nApproximate solution of %s is xn=
$11.9f on %drd iterations \n\n',y, p0, i);
elseif i == 1
fprintf('\nApproximate solution of %s is xn=
expand button
Transcribed Image Text:NEWTON-RAPHSON METHOD EXAMPLE 1: Find the root of the function f(x) = cos(x) using NRM having initial approximation of 1 Input the following codes to your MATLAB edit window and name as 'newton.m" * Newton-Raphson Algorithm syms x Input section y = input ('Enter the given function: '); yd = input ('Enter the derivative of the given function: '); p0 = input ('Enter initial approximation: '); input ('Enter no. of iterations, n:'); tol = input('Enter tolerance, tol: '); n = i = 1; while i <= n d= (eval (subs (y,x,p0)))/eval(subs (yd, x, p0)); p0 = p0 if abs (d) < tol if i == 3 d; || fprintf('\nApproximate solution of %s is xn= $11.9f on %drd iterations \n\n',y, p0, i); elseif i == 1 fprintf('\nApproximate solution of %s is xn=
end
end
Run the program and enter the following
Enter the given function: cos(x)
Enter the derivative of the given function: sin(x)
Enter initial approximation: 1
Enter no. of iterations, n: 30
Enter tolerance, tol: 0.0001
Write the output below
expand button
Transcribed Image Text:end end Run the program and enter the following Enter the given function: cos(x) Enter the derivative of the given function: sin(x) Enter initial approximation: 1 Enter no. of iterations, n: 30 Enter tolerance, tol: 0.0001 Write the output below
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