newton
Newton's method for solution of nonlinear equations.
` x=newton(f, xin)`
` (x, it, success)=newton(f, xin, showit, itmax, tol)`
 Inputs `f` The function of the form `[y,dy]=f(x)` which returns the value of the function `y=g(x)` for the solution of `g(x)=0` as well as the derivative or the Jacobian of the function. `xin` An initial estimate of the solution. `showit` If `true` the progress of iterations is displayed. `itmax` The maximum number of iterations allowed. `tol` The criterion for convergence of the iterations, i.e, if the norms of the estimated solution in two successive iterates differ by less than `tol` the iterations are terminated. Outputs `x` The computed solution, if the iterations converge. `it` The number of iterations required. `success` `true` if the iterations converge, and `false` otherwise.

Example
```>>function (y,dy)=func(x)
>	x1=x,x2=x,x3=x
>	x1x2=x1*x2
>	x2x3=x2*x3
>	expx1x2=exp(-x1x2)
>	y=[3x1-cos(x2x3)-.5
>	   x1^2-81(x2+.1)^2+sin(x3)+1.06
>           expx1x2+20x3+(10pi-3)/3]
>	dy=[3,x3*sin(x2x3),x2*sin(x2x3)
>            2x1   -162(x2+.1)   cos(x3)
>            -x2*expx1x2  -x1*expx1x2  20]
>end
>>x=newton(\$func,rand(3,1),1)
Iteration 1 x norm     0.521957 y norm    15.358967
Iteration 2 x norm     0.523525 y norm     0.492632
Iteration 3 x norm     0.523598 y norm     0.046902
Iteration 4 x norm     0.523599 y norm     0.000644
Iteration 5 x norm     0.523599 y norm     0.000000
>>x,NL
0.5
3.2062e-016
-0.5236

>>func(x)
Scaled by 10^-14
0
-0.5107
-0.1776

```