07/25/2010, 11:25 PM
ok in a recurrence equation we iterate.
but how ?
you said x_0 = 0 ok.
again how ? and does that really converge ?? why ?
to quote :
"You compute values of f along suitably dense grid on the y-Axis by using these values on the y-Axis with a numeric integration."
that sounds vague and mysterious to me.
so lets say we use dummy variables : f(i) = a , f(2i) = b , f(3i) = c
but approaching an integral from -oo to + oo with a few integer points of dummy variables ?
i even doubt if numeric integration is a good approximation of the whole integral !? afterall it goes from -oo to + oo.
am i correct in assuming you use dummy variables for the values of f(i) , f(2i) etc and then try to solve it by replacing the integral on the RHS with " rectangles " and the dummy variables ?
and then further try to control those dummy variables by placing upper and lower bounds on their values ?
is f(i) , f(2i) , f(3i) , ... a good choice or do you mean suitable dense rather as in " the rationals are dense in the reals " ?
is f(a/b i) for all a and b rel prime up to value 100 a good choice for dummy variables ?
is the recurrence equation suppose to give exact values or upper and lower boundaries ?
assuming convergence - hence existance - , how is this necc unique ?
can you proof the recurrence to have a single unique solution ?
( maybe that one is easy , i havent really tried that yet )
sorry if im slow , on the other hand i would be amazed to be alone with my doubts or misunderstandings.
regards
tommy1729
but how ?
you said x_0 = 0 ok.
again how ? and does that really converge ?? why ?
to quote :
"You compute values of f along suitably dense grid on the y-Axis by using these values on the y-Axis with a numeric integration."
that sounds vague and mysterious to me.
so lets say we use dummy variables : f(i) = a , f(2i) = b , f(3i) = c
but approaching an integral from -oo to + oo with a few integer points of dummy variables ?
i even doubt if numeric integration is a good approximation of the whole integral !? afterall it goes from -oo to + oo.
am i correct in assuming you use dummy variables for the values of f(i) , f(2i) etc and then try to solve it by replacing the integral on the RHS with " rectangles " and the dummy variables ?
and then further try to control those dummy variables by placing upper and lower bounds on their values ?
is f(i) , f(2i) , f(3i) , ... a good choice or do you mean suitable dense rather as in " the rationals are dense in the reals " ?
is f(a/b i) for all a and b rel prime up to value 100 a good choice for dummy variables ?
is the recurrence equation suppose to give exact values or upper and lower boundaries ?
assuming convergence - hence existance - , how is this necc unique ?
can you proof the recurrence to have a single unique solution ?
( maybe that one is easy , i havent really tried that yet )
sorry if im slow , on the other hand i would be amazed to be alone with my doubts or misunderstandings.
regards
tommy1729