## newton_system2_pseudocode.txt

function newton_system2 ( f, fp, x, xtol, ftol, itmax )

it = 0
DX = 0 
alpha = 0

Begin loop

  it = it + 1

  Set Xold to X
  Set DXold to DX
  Evaluate F(X) and DF(X)
  Solve for DX: DF(X) * DX = - F(X)
  Set X = X + DX

  Set alpha_old to alpha
  if ||DX_old|| is not 0, set alpha to ||DX|| / ||DX_old|| 
    if alpha_old is not 0, set r = log ( alpha ) / log ( alpha_old )

  if ||DX|| is less than xtol and ||F(X)|| is less than ftol, success
  if it > itmax, failure

End loop