Talk:Numerical integration/Gauss-Legendre Quadrature: Difference between revisions
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(Idle musing on preserving irrational values in intermediate calculations) |
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::: Yeah but 1) Legendre polynomial roots are not always rational; 2) it's sloooow, if you go down that route, you might as well use some other way to do integrals. --[[User:Ledrug|Ledrug]] 14:32, 28 June 2011 (UTC) |
::: Yeah but 1) Legendre polynomial roots are not always rational; 2) it's sloooow, if you go down that route, you might as well use some other way to do integrals. --[[User:Ledrug|Ledrug]] 14:32, 28 June 2011 (UTC) |
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:::: Idle musing...say you've got a scenario where your root may not be rational. If greater precision in the results may be needed later, but not now, one might save off the polynominal factoring routine's state for resumption later, no? I'm not saying it's necessarily useful for this task, just thinking about scenarios where irrational numbers in intermediate calculations might have their precision preserved. --[[User:Short Circuit|Michael Mol]] 15:35, 28 June 2011 (UTC) |
:::: Idle musing...say you've got a scenario where your root may not be rational. If greater precision in the results may be needed later, but not now, one might save off the polynominal factoring routine's state for resumption later, no? I'm not saying it's necessarily useful for this task, just thinking about scenarios where irrational numbers in intermediate calculations might have their precision preserved. --[[User:Short Circuit|Michael Mol]] 15:35, 28 June 2011 (UTC) |
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::::: Hmm, not necessarily. For polys higher than degree 5, there are no general analytical way to get roots, so all you have left is numerical solutions. You could try to use rationals during <i>that</i>, for example while using Newton's method, but often there are so many iterations, your rational representation will grow too fast to be of much realistic use. --[[User:Ledrug|Ledrug]] 15:44, 28 June 2011 (UTC) |
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== Tables and layout == |
== Tables and layout == |
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