AERN-RnToRm-0.3.0.1: polynomial function enclosures (PFEs) approximating exact real functions

Portability portable experimental mik@konecny.aow.cz

Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.Elementary

Description

Internal module for Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.

Implementation of elementary functions applied to polynomials.

Synopsis

# Documentation

Arguments

 :: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box) => Int maximum polynomial degree -> EffortIndex ?? -> ERChebPoly box b -> (ERChebPoly box b, ERChebPoly box b)

Approximate the pointwise square root of a polynomial by another polynomial from below and from above.

Arguments

 :: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box) => Int maximum polynomial degree -> EffortIndex minimum approx Taylor degree -> ERChebPoly box b -> (ERChebPoly box b, ERChebPoly box b)

Approximate the pointwise exponential of a polynomial by another polynomial from below and from above.

Arguments

 :: (ERRealBase b, Integral i, DomainBox box varid Int, Ord box) => Int maximum polynomial degree -> ERChebPoly box b -> i -> ERChebPoly box b

Approximate the pointwise integer power of a polynomial by another polynomial from above.

Arguments

 :: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box) => Int maximum polynomial degree -> EffortIndex ?? -> ERChebPoly box b -> (ERChebPoly box b, ERChebPoly box b)

Approximate the pointwise natural logarithm of a polynomial by another polynomial from below and from above.

Arguments

 :: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box) => Bool True iff sine, False iff cosine -> Int maximum polynomial degree -> EffortIndex minimum approx Taylor degree -> ERChebPoly box b -> (ERChebPoly box b, ERChebPoly box b)

Approximate the pointwise sine of a polynomial by another polynomial from below and from above.

Arguments

 :: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box) => Int maximum polynomial degree -> EffortIndex minimum approx degree -> ERChebPoly box b -> (ERChebPoly box b, ERChebPoly box b)

Approximate the pointwise cosine of a polynomial by another polynomial from below and from above using the tau method as described in [Mason & Handscomb 2003, p 62].