nag_quad_md_numth_coeff_2prime (d01gzc) calculates the optimal coefficients for use by
nag_quad_md_numth_vec (d01gdc),
when the number of points is the product of two primes.
Korobov (1963) gives a procedure for calculating optimal coefficients for
-point integration over the
-cube
, when the number of points is
where
and
are distinct prime numbers.
The advantage of this procedure is that if
is chosen to be the nearest prime integer to
, then the number of elementary operations required to compute the rule is of the order of
which grows less rapidly than the number of operations required by
nag_quad_md_numth_coeff_prime (d01gyc). The associated error is likely to be larger although it may be the only practical alternative for high values of
.
The optimal coefficients are returned as exact integers (though stored in a double array).
Not applicable.
The time taken by nag_quad_md_numth_coeff_2prime (d01gzc) grows at least as fast as
. (See
Section 3.)
This example calculates the Korobov optimal coefficients where the number of dimensons is and the number of points is the product of the two prime numbers, and .
None.