Timeline for Accelerating convergence for some double sums
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| May 27, 2022 at 9:14 | vote | accept | F. C. | ||
| May 19, 2022 at 22:21 | history | edited | Somos | CC BY-SA 4.0 |
Removed word.
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| May 19, 2022 at 22:05 | history | edited | Somos | CC BY-SA 4.0 |
Added link to Math.Comp.
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| May 19, 2022 at 21:53 | comment | added | Jorge Zuniga | @Somos. Reference: H. Monien Math. Comp. 79 (2010), 857-869 "Gaussian quadrature for sums: A rapidly convergent summation scheme" ams.org/journals/mcom/2010-79-270/S0025-5718-09-02289-3/… | |
| May 19, 2022 at 18:10 | history | edited | Somos | CC BY-SA 4.0 |
Added link to Monien paper.
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| May 19, 2022 at 17:03 | history | edited | Somos | CC BY-SA 4.0 |
Added mention of summonien.
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| May 19, 2022 at 16:42 | comment | added | Jorge Zuniga | @Somos. Monien summation is much faster. p(n) = binomial(n+1,2); Y(k,b) = sumnummonien(l=1, (2*l+1)/(p(k)+p(l))^b,sumtable); Z(a,b) = sumnummonien(k=1, (2*k+1)/p(k)^aY(k,b)); default(realprecision,57); sumtable = sumnummonieninit(); print(2*Z(2,2)+4*Z(1,3)) /** 15.9999999999999999999999999999999999999999999999999999999, time = 16 ms. **/ | |
| May 19, 2022 at 15:15 | history | edited | Somos | CC BY-SA 4.0 |
Added sumnuminit suggested by Henri Cohen.
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| May 19, 2022 at 12:02 | comment | added | Henri Cohen | @Somos: when you have double sums or double integrals, it is preferable to initialize nodes and weights once and for all for the inner sum. So if you set tab=sumnuminit() and write Y(k,b)=sumnum(l=0,(2*l+3)/(p(k)+p(l))^b,tab) the result will be obtained much faster (3 times at 57 decimals): note that the sumnuminit() command must be performed AFTER setting the precision to 57. | |
| May 19, 2022 at 11:06 | history | edited | Somos | CC BY-SA 4.0 |
Changed sumpos to sumnum. Rewording.
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| May 18, 2022 at 17:06 | comment | added | François Brunault | @F.C. The recent book "Numerical algorithms for number theory - Using PARI/GP" by Belabas and Cohen discusses numerical summation in chapter 4, it also provides open-source programs. The relevant programs, besides sumpos, include SumLagrange and SumSidi. | |
| May 18, 2022 at 11:35 | history | edited | Somos | CC BY-SA 4.0 |
Move one line of code down.
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| May 18, 2022 at 8:13 | comment | added | F. C. | Thanks, very nice to see that open-source pari can do that. | |
| May 18, 2022 at 2:49 | history | answered | Somos | CC BY-SA 4.0 |