C++/matlab programming

Quote:

Originally Posted by anncar

So I am given three non linear equations:

Code:

x1(x2-2)=0, x2(x3-3)=0, x3(x1-1)=0

and i need to solve using newtons method using 100 randomly selected initial guesses for x1^(0), x2^(0) and x3^(0).

First find the Jacobian:

$<br /> J(x_1,x_2,x_3)=\left[ \begin{array}{ccc}x_2-2&x_1&0\\<br /> 0&x_3-3&x_2\\<br /> x_3&0&x_1-1 \end{array}\right]<br />$

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

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

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

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

Then the general itteration step is:

solve:

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

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

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

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

dP=J\P

if I recall correctly

RonL