| In this thesis we show that the Euler type algorithms find (i) a complex number z such that (VBAR)f(z)(VBAR) 0, approximately, with 6672(d(d+log(VBAR)log (epsilon)(VBAR))M(26(d+(VBAR)log (epsilon)(VBAR)) binary bit operations, (ii) an approximate zero for a polynomial of degree d without multiple roots with average bit complexity approximately, 6672(d M(26d))) binary bit operations, where M(n) denotes the bit complexity for the multiplication of two n-digit numbers. |
