| Topic: |
Science > Physics |
| User: |
"Luna Laurent" |
| Date: |
23 Jul 2007 12:22:38 AM |
| Object: |
How to evaluate Norlund Rice integral? |
Hi all,
I am interested in evaluating the third integral on this page:
http://www.answers.com/topic/n-rlund-rice-integral
which is a line integral, called the Norlund Rice integral.
I have a complicated function f(z) in that integrand.
I can do a normal numerical integral for that, it is a little bit slow.
I am interested in fast evaluation of such integral, and good approximations
for such integral for large n, and any other tricks in fast evaluation of
such integral, with good precision.
Comments and suggestions are much appreciated! Thank you!
.
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| User: "Androcles" |
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| Title: Re: How to evaluate Norlund Rice integral? |
23 Jul 2007 05:14:32 AM |
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"Luna Laurent" <luna_laurent@yahoo.com> wrote in message
news:f81e2v$mbq$1@news.Stanford.EDU...
: Hi all,
:
: I am interested in evaluating the third integral on this page:
:
: http://www.answers.com/topic/n-rlund-rice-integral
:
: which is a line integral, called the Norlund Rice integral.
:
: I have a complicated function f(z) in that integrand.
:
: I can do a normal numerical integral for that, it is a little bit slow.
:
: I am interested in fast evaluation of such integral, and good
approximations
: for such integral for large n, and any other tricks in fast evaluation of
: such integral, with good precision.
:
: Comments and suggestions are much appreciated! Thank you!
:
The most logical and simplest answer is: Get a faster computer.
.
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| User: "Salmon Egg" |
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| Title: Re: How to evaluate Norlund Rice integral? |
23 Jul 2007 11:46:57 AM |
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On 7/22/07 10:22 PM, in article f81e2v$mbq$1@news.Stanford.EDU, "Luna
Laurent" <luna_laurent@yahoo.com> wrote:
Hi all,
I am interested in evaluating the third integral on this page:
http://www.answers.com/topic/n-rlund-rice-integral
which is a line integral, called the Norlund Rice integral.
I have a complicated function f(z) in that integrand.
I can do a normal numerical integral for that, it is a little bit slow.
I am interested in fast evaluation of such integral, and good approximations
for such integral for large n, and any other tricks in fast evaluation of
such integral, with good precision.
Comments and suggestions are much appreciated! Thank you!
Off hand it seems like the sum is easier to calculate than the integral. Why
do you want to go through the trouble of doing the integral instead of the
sum?
Bill
--
Support the troops. Impeach Bush. Oh, I forgot about Cheney.
.
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| User: "Luna Laurent" |
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| Title: Re: How to evaluate Norlund Rice integral? |
23 Jul 2007 10:32:41 PM |
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"Salmon Egg" <salmonegg@sbcglobal.net> wrote in message
news:C2CA2991.8C0EC%salmonegg@sbcglobal.net...
On 7/22/07 10:22 PM, in article f81e2v$mbq$1@news.Stanford.EDU, "Luna
Laurent" <luna_laurent@yahoo.com> wrote:
Hi all,
I am interested in evaluating the third integral on this page:
http://www.answers.com/topic/n-rlund-rice-integral
which is a line integral, called the Norlund Rice integral.
I have a complicated function f(z) in that integrand.
I can do a normal numerical integral for that, it is a little bit slow.
I am interested in fast evaluation of such integral, and good
approximations
for such integral for large n, and any other tricks in fast evaluation of
such integral, with good precision.
Comments and suggestions are much appreciated! Thank you!
Off hand it seems like the sum is easier to calculate than the integral.
Why
do you want to go through the trouble of doing the integral instead of the
sum?
Bill
--
Support the troops. Impeach Bush. Oh, I forgot about Cheney.
Because the sum is out of the precision of double. Look at the Binomial
coefficents, they can be super large. Can you do that in double precision?
And the sum is alternating and final result has to be very small and
accurate.
.
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| User: "Salmon Egg" |
|
| Title: Re: How to evaluate Norlund Rice integral? |
24 Jul 2007 12:27:45 AM |
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On 7/23/07 8:32 PM, in article f83s0n$d8i$1@news.Stanford.EDU, "Luna
Laurent" <luna_laurent@yahoo.com> wrote:
Off hand it seems like the sum is easier to calculate than the integral.
Why
do you want to go through the trouble of doing the integral instead of the
sum?
Bill
--
Support the troops. Impeach Bush. Oh, I forgot about Cheney.
Because the sum is out of the precision of double. Look at the Binomial
coefficents, they can be super large. Can you do that in double precision?
And the sum is alternating and final result has to be very small and
accurate.
I have not looked at the problem as a solver. Using Maple, you should be
able to use hundreds of decimal places in your calculations. You still may
still be limited roundoff error. Have you looked at combining pairs of terms
analytically?
Bill
--
Iraq: About three Virginia Techs a month
.
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| User: "Luna Laurent" |
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| Title: Re: How to evaluate Norlund Rice integral? |
24 Jul 2007 06:30:20 AM |
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"Salmon Egg" <salmonegg@sbcglobal.net> wrote in message
news:C2CADBE1.8C47B%salmonegg@sbcglobal.net...
On 7/23/07 8:32 PM, in article f83s0n$d8i$1@news.Stanford.EDU, "Luna
Laurent" <luna_laurent@yahoo.com> wrote:
Off hand it seems like the sum is easier to calculate than the integral.
Why
do you want to go through the trouble of doing the integral instead of
the
sum?
Bill
--
Support the troops. Impeach Bush. Oh, I forgot about Cheney.
Because the sum is out of the precision of double. Look at the Binomial
coefficents, they can be super large. Can you do that in double
precision?
And the sum is alternating and final result has to be very small and
accurate.
I have not looked at the problem as a solver. Using Maple, you should be
able to use hundreds of decimal places in your calculations. You still may
still be limited roundoff error. Have you looked at combining pairs of
terms
analytically?
Bill
--
Iraq: About three Virginia Techs a month
Speed is a huge concern so multiple precision or symbolic is not a choice.
.
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