ABSTRACT
The evaluation of Eq. (4.16a) requires (0 + I + 2 + 3 + 4) = 10 multiplications and four additions; the evaluation of Eq. (4.16b) requires (2 + 3 + 4) = 9 multiplications and three additions; and the evaluation of Eq. (4.16c) requires (1 + 2 + 3 + 4 + 5) = 15 multiplications, four divisions, and five additions. This is a modest amount of work, even for polynomials of degree as high as 10. However, if a polynomial must be evaluated many times, or many polynomials must be evaluated, or very high degree polynomials must be evaluated, a more efficient procedure is desirable. The nested multiplication algorithm is such a procedure.
