Approximating a definite integral of product of cosines to within an
accuracy of n binary digits where the integrand depends on input
integers x[k] given in binary radix, is equivalent to counting the
number of equal-sum partitions of the integers and is thus a #P problem.
Similarly, integrating this function from zero to infinity and deciding
whether the result is either zero or infinity is an NP-Complete problem.
Efficient numerical integration methods such as the double exponential
formula and the sinc approximation have been around since the mid 70's.
Noting the hardness of approximating the integral we argue that the
proven rates of convergence of such methods cannot possibly be correct
since they give rise to an anomalous result as P=#P.
|State||Published - 2015|
- Computer Science - Numerical Analysis
- Computer Science - Computational Complexity