# Thread: nonlinear systems of equations

1. ## nonlinear systems of equations

Need help with steps to the answer
Solve the following nonlinear system
3x - cos(yz) - 1/2 = 0
$x^2-81(y+0.1)^2 + sin z+1.06 = 0
$

$e^{-xy}+20z + (10\pi - 3)/3 = 0
$

$x^{(0)}= 0.1 y^{(0)}= 0.1 z^{(0)}= -0.1
$

Need help with steps to the answer
Solve the following nonlinear system
3x - cos(yz) - 1/2 = 0
$x^2-81(y+0.1)^2 + sin z+1.06 = 0
$

$e^{-xy}+20z + (10\pi - 3)/3 = 0
$

$x^{(0)}= 0.1 y^{(0)}= 0.1 z^{(0)}= -0.1
$
You do know Newton-Raphson for a system don't you?

$X_{n+1}=X_n-[J(X_{n-1})]^{-1}F(X_n)$

where $X_n$ is a column vector as is $F(X_n)$ and $J(X_n)$ is the Jacobian of $F$ at $X_n$.

CB