`We discuss now the computational cost for evaluating
the Taylor polynomial value at some point
`

`When evaluating the compiler (usually) translates it
to multiplications. Thus, the naive algorithm
`

p = b(0) do i=1,n p = p + b(i)*x**i end do

`A better alternative is to save the computed power of
from one iteration to the next. Since
,
iteration will need just two multiplications
(not ) to compute .
`

p = b(0) powx = 1.0 do i=1,n powx = powx*x ! powx = x**i p = p + b(i)*powx end do

`We can do even better than this, by rewriting the polynomial
in nested form
`

`We have to start with the last term and loop back to the first.
The algorithm goes as follows
`

p = b(n) do i=n-1,0,-1 p = b(i) + x*p end do

`and requires additions and only multiplications.
`

`
`

Adrian Sandu 2001-08-26