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.Bounds

Description

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

Implementation of various functions related to the bounds of polynomials.

Synopsis

# Documentation

Arguments

 :: (ERRealBase b, DomainBox box varid Int, Ord box) => EffortIndex how hard to try -> ERChebPoly box b -> b

Find an upper bound on a polynomial over the unit domain [-1,1]^n.

Arguments

 :: (ERRealBase b, DomainBox box varid Int, Ord box, DomainBoxMappable boxb boxbb varid b [(b, b)], Num varid, Enum varid) => EffortIndex how hard to try -> ERChebPoly box b -> b

Find a close upper bound on an affine polynomial over the unit domain [-1,1]^n.

Arguments

 :: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box, DomainBoxMappable boxra boxras varid (ERInterval b) [ERInterval b], DomainBoxMappable boxra boxra varid (ERInterval b) (ERInterval b), DomainIntBox boxra varid (ERInterval b), Num varid, Enum varid) => EffortIndex how hard to try looking for peaks -> ERChebPoly box b -> b

Find a close upper bound on a quadratic polynomial over the unit domain [-1,1]^n.

Arguments

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

Approximate from below and from above the pointwise maximum of two polynomials

Arguments

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

Approximate the function max(0,p(x)) by a polynomial from below and from above.

Arguments

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

A version of `chplNonneg` using a cubic approximation.