The main goal in the development of the new algorithm for adaptive
multidimensional integration was to improve the reliability of some
previous algorithms. Tests [9] of a FORTRAN implementation, DCUHRE, have
shown that this goal has been achieved. The new algorithm has been
structured to allow its efficient implementation on shared memory parallel
computers and good speedups are demonstrated in the test report [9].
In each dimension more than one integration rule is made available to the
user because the relative performance of different rules may differ from
one problem to another.
The
other additional feature of the new algorithm are the modifications that allow
its application to a vector of similar integrals over a common integration
region. This feature should be used
with caution, because the algorithm chooses a subdivision of the integration
region that may be refined according to the behavior of particular
integrands which have certain local regions of difficulty.
If the integrands in a vector of integrands are significantly different,
the vector should probably be split into smaller vectors of integrands
and the algorithm applied separately to each subvector.
For integrands that have enough similarity, the new algorithm may save both
time and space because of the common subdivision, and will also allow for
additional saving in time on many types of parallel computers where the
integrand function evaluations can be done in parallel.