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Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.Integration | Portability | portable | Stability | experimental | Maintainer | mik@konecny.aow.cz |
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Description |
Internal module for Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.
Implementation of safely rounded integration of polynomials
and other related functions.
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Synopsis |
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chplIntegrate :: (ERRealBase b, DomainBox box varid Int, Ord box) => varid -> ERChebPoly box b -> (ERChebPoly box b, ERChebPoly box b) | | chplVolumeAboveZero :: (ERRealBase b, DomainBox box varid Int, Ord box, DomainBoxMappable boxb boxbb varid b [(b, b)]) => [varid] -> ERChebPoly box b -> (b, b) | | chplDifferentiate :: (ERRealBase b, DomainBox box varid Int, Ord box) => ERChebPoly box b -> varid -> ERChebPoly box b |
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Documentation |
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:: (ERRealBase b, DomainBox box varid Int, Ord box) | | => varid | variable to integrate by
| -> ERChebPoly box b | | -> (ERChebPoly box b, ERChebPoly box b) | | Approximate from below and from above the integral of a polynomial.
Based on the following formulas for Chebyshev polynomials:
\int T_n(x)dx =
T_{n+1}(x)/2(n+1) - T_{n-1}(x)/2(n-1)
\int T_1(x)dx =
T_2(x)/4 + 1/4
\int T_0(x)dx =
T_1(x)
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measure the volume between a polynomial and the zero axis on [-1,1]^n
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Produced by Haddock version 2.1.0 |