zetafunction
Jun8-09, 09:36 AM
the idea is let be D the unit sphere on R^3
then i wanna compute the following integral \iint _{D} f(x,y,z)
then in order to obtain an approximate value , i make a change of variable to polar coordinates and replace the integral over angular variables by a sum so my approximate value of the integral is
\sum_ {i} \int_{0}^{1}dr f(r, \omega _{i})g(\omega _u )
then instead of a triple integral i have just a 1-D integral over 'r' and a sum over angular variables.
i know this can be done but is the approximation good ? , i mean if there is numerical unstabilities or you should take too many approximations over the angles.
then i wanna compute the following integral \iint _{D} f(x,y,z)
then in order to obtain an approximate value , i make a change of variable to polar coordinates and replace the integral over angular variables by a sum so my approximate value of the integral is
\sum_ {i} \int_{0}^{1}dr f(r, \omega _{i})g(\omega _u )
then instead of a triple integral i have just a 1-D integral over 'r' and a sum over angular variables.
i know this can be done but is the approximation good ? , i mean if there is numerical unstabilities or you should take too many approximations over the angles.