Question

use matlab coding

and do it with Newton- Raphson Method

The Gauss-Seidel method is also known as the method of successive displacements. To illustrate the logics, a flowchart is developed in Figure 1 (instructed in the lecture too) x = g(x) k=0 rk) is not the root rfk) is the root k=k+1 . Figure 1 Flowchart of Gauss-Seidel iterative method

Answer 1

%type the following function in matlab to get the result for solving
%polynomial using newton raphson method

function root=find_root(coef)

len=length(coef); %number of coefficients of polynomial.
x=100; % initial guess
error=inf;

while(error>0.00001) %precision llimit
y=0;
ydif=0;
for n=0:len-1
y=y+coef(len-n)*x^n; %calculating polynomial value
ydif=ydif+n*coef(len-n)*x^(n-1); %calculate derivative value
end
error=y/ydif; %error caluclation
x=x-y/ydif; %updated value
end
fprintf('value of root x for polymonimal is x=%d',x);
x

type the following function in matlab to get the result for solving polynomial using newton raphson method function root-find root (coef) len-length (coef)number of coefficients of polynomial x-100; initial guess error-inf: while (error>0.00001) %precision ïïīmít y#0 ; ydif-o: for n-0:len-1 ysy+c oef (1en-n)*Χ' n; %calculating ydif-yd 11+nīcoef (len-n) #x. (n-1) ; calculate end error-y/ydif: tetror caluclation x-x-y/ ydif; %updated value polynomial value derivative value end fprintf( 'value of root x for polymo nimaï ïs x-%d',x);

for example
If you want to find a root of
f(x)=12x^3+8x^2-3x^1+88,
write the command window of matlab as calling the function -

find_root([88 -3 8 12]);

Command Window >> find root (l88 -3 8 12]); value of root x for polymonimal is x--6.734635e-01 -0.6735

hence you see the root is -0.6735 for the assumed ploynomial...

similarly you can test for other polynomial by varying coeffiect of any degree of polynomial and also change the error precision to vary the accuracy of the result.

good luck.