On the Parallel Evaluation of Polynomials

If an unlimited number of processors is available, then for any given number of steps s, s≥1, polynomials of degree as large as C2 n-δ can be evaluated, where C= √2 and δ ≈ √2s. This implies polynomials of degree can be evaluated in log <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> n+√2log <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> n +0(1) steps. Various techniques for the evaluation of polynomials in a "reasonable number" of "steps" are compared with the known lower bounds.