This question is about Numerical Mathematics and Computing.I am not familiar wit

Question

This question is about Numerical Mathematics and Computing.I am not familiar with matlab...Please give me a code with matlab and with a short explain if you like.Thank you soooooooo much and I will give you a good thumb if the answer is correct or nearly correct.

the lecture note is here(it is use to tell you how to solve problem like this one, I know the note and know how to solve these kind of problem, but I do not know what this problem meaning and how to use matlab to solve it..):

Problem 4. (20%) C the example of solving a system of nonlinear equations onsider by Newton's method, as given on Pages 95-97 of the Lecture notes. Write a program to carry out this iteration, using Gauss elimination to solve the 2 by 2 linear systems that arise. Use each of the following 16 initial data sets for the Newton iteration: (0) (0) (i, j), i 0,1, 2, 3, j-0, 1,2,3 Present and discuss your numerical results in a concise manner

Explanation / Answer

clc;
clear all;

x1=2; x2=2; %initial guess

n=0;
while(n<5)
f1=x1^2*x2-1; % your g1
f2=x2-x1^4; % your g2

f11=2*x1*x2
f12=x1^2;

f21=-4*x1^3;
f22=1;

J=[f11 f12 ; f21 f22]; %jacobian matrix
J1=inv(J); %inverse of jacobi
%J1*[f1; f2];
Z=[x1;x2]-J1*[f1; f2]; %newton formula
n=n+1 %next interation
%next interation intial guess
x1=Z(1);
x2=Z(2);
Z
end

% reuslts

n =

1

Z =

1.5368
1.1765

n =

2

Z =

1.2156
0.9151

n =

3

Z =

1.0422
0.9378

n =

4

Z =

1.0012
0.9944

n =

5

Z =

1.0000
1.0000

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