 | AERN-RnToRm-0.4.9.1: polynomial function enclosures (PFEs) approximating exact real functions | Source code | Contents | Index |
| Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.Integration |
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Internal module for Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.
Implementation of safely rounded integration of polynomials and other related functions.
| chplIntegrate :: (ERRealBase b, DomainBox box varid Int, Ord box) => varid -> ERChebPoly box b -> (ERChebPoly box b, ERChebPoly box b) |
| chplIntegrate | Source |
| :: (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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