So I am given three non linear equations:

and i need to solve using newtons method using 100 randomly selected initial guesses for x1^(0), x2^(0) and x3^(0).Code:`x1(x2-2)=0,`

x2(x3-3)=0,

x3(x1-1)=0

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- Jan 21st 2008, 01:40 PManncarC++/matlab programming
So I am given three non linear equations:

Code:`x1(x2-2)=0,`

x2(x3-3)=0,

x3(x1-1)=0

- Jan 21st 2008, 10:09 PMCaptainBlack
First find the Jacobian:

$\displaystyle

J(x_1,x_2,x_3)=\left[ \begin{array}{ccc}x_2-2&x_1&0\\

0&x_3-3&x_2\\

x_3&0&x_1-1 \end{array}\right]

$

Now Newton's method proceeds from a initial approximation of guess: $\displaystyle P_{(0)}$ to the next approximation using by solving:

$\displaystyle J(P_{(0)}) \delta P = F(P_{(0)})$

for $\displaystyle \delta P$, then the next estimate is:

$\displaystyle P_{(1)}=P_{(0)}+ \delta P$.

Then the general itteration step is:

solve:

$\displaystyle J(P_{(n)}) \delta P = F(P_{(n)})$

for $\displaystyle \delta P$, then the next estimate is:

$\displaystyle P_{(n+1)}=P_{(n)}+ \delta P$.

In Matlab the equation J dP= P is solved using a statement of the form:

dP=J\P

if I recall correctly

RonL