Accuracy and error analysis (was Re: [Maxima] primes)

Albert Reiner wrote:

>
>At any rate, I would hope that any error-propagating scheme someone
>might come up with is not integrated as tightly into Maxima as is the
>case for Mma.
>  
>

There are specific, helpful, less pessimistic results such as ..

evaluate a polynomial  p(x)=an*x^n+ ...+a0   by horner's rule,  assume 
an, ... a0 are exact, but
x has error e.
there is an explicit formula based on evaluating q(x)  where q is dp/dx 
with all coefficients made positive,
for the error in evaluating p.

To the extent that you can make your problem into evaluating polynomials 
or ratios of them,
you can get error bound for a cost approximately 2X the cost of merely 
evaluating.

See http://www.cs.berkeley.edu/~fateman/papers/polyval.pdf
for example.
RJF

>maxima
>  
>