I'm trying to understand Laguerre's method for root finding and I have hit one road block.
Suppose I have a polynomial $p(x) = x^4 + 1$ and an initial guess $x_0 = 0$. This results in division by zero in the above formula.
What to do in such cases? Should one backtrack and try again with different guess? Are there any guides on how to pick the next $x_k$?
"Numerical Recipes" contain a test for the zero division, in which case, the next step becomes
polar(1+abx, iter), where
abx is computed above and
iter is the number of iteration. Does anyone know what does that
polar(1+..., iter) mean? Why does it use polar coordinates?