Error estimates in the Gauss-Kronrod rule
- To: mathgroup at smc.vnet.net
- Subject: [mg127010] Error estimates in the Gauss-Kronrod rule
- From: João Paulo Pereira <joaopereira9 at gmail.com>
- Date: Sat, 23 Jun 2012 04:17:29 -0400 (EDT)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
Hi there, I need some information regarding the Gauss-Kronrod rule data provided by Mathematica. When we write NIntegrate`GaussKronrodRuleData[n, precision], we get the gauss-kronrod nodes, weights and an error estimate. In this link http://reference.wolfram.com/mathematica/tutorial/NIntegrateIntegrationRules.html it is explained how this rule can be applied through the example: Total@MapThread[{f[#1] #2, f[#1] #3} &, {absc, weights, errweights}] understand with {absc, weights, errweights} = NIntegrate`GaussKronrodRuleData[n, precision] It also explains that "The command (...) implements the integration rule weighted sums for the integral estimate, , and the error estimate, , where are the abscissas, are the weights, and are the error weights." I know how to compute the nodes and I do get the same values as Mathematica's but I haven't been able, so far, to figure out how the are computed. I need to understand this for the program I'm writing and it seems Mathematica's Help does not provide any explanation on the subject. Can someone point me to the reference (article, etc ) from which I can understand how this Methematica command computes the error weights estimates? Thanks in advance Jo=E3o Pereira