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BernsteinBasis

Bernstein polynomials on an interval

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

BernsteinBasis(k, n, a, b, x)

Parameters

k

-

algebraic expression; the index

n

-

algebraic expression; the degree

a

-

algebraic expression; left end of interval

b

-

algebraic expression; right end of interval

x

-

algebraic expression; the argument

Description

• 

BernsteinBasisk,n,a,b,x=nkbxnkxakban defines the kth Bernstein polynomial of degree n which is nonnegative on the interval a,b.

• 

At present, this can only be evaluated in Maple by prior use of the object-oriented representation obtained by P:=convert(p,MatrixPolynomialObject,x) and subsequent call to P:-Value(<x-value>), which uses the de Casteljau algorithm to evaluate the polynomial p.

Examples

p3BernsteinBasis0&comma;4&comma;0&comma;1&comma;x&plus;5BernsteinBasis2&comma;4&comma;0&comma;1&comma;x&plus;7BernsteinBasis4&comma;4&comma;0&comma;1&comma;x

p3BernsteinBasis0&comma;4&comma;0&comma;1&comma;x&plus;5BernsteinBasis2&comma;4&comma;0&comma;1&comma;x&plus;7BernsteinBasis4&comma;4&comma;0&comma;1&comma;x

(1)

Pconvertp&comma;MatrixPolynomialObject&comma;x

PRecordValue&equals;Defaultvalue&comma;Variable&equals;x&comma;Degree&equals;4&comma;Coefficient&equals;coe&comma;Dimension&equals;1&comma;1&comma;Basis&equals;BernsteinBasis&comma;BasisParameters&equals;4&comma;0&comma;1&comma;IsMonic&equals;mon&comma;OutputOptions&equals;shape&equals;&comma;storage&equals;rectangular&comma;order&equals;Fortran_order&comma;fill&equals;0&comma;attributes&equals;

(2)

P:-Degree

4

(3)

Note that the result returned by convert(...,MatrixPolynomialObject) represents a matrix polynomial; hence these results are 1 by 1 matrices.

P:-Value0

3

(4)

P:-Value1

7

(5)

P:-Value0.3

2.100000000

(6)

factorP:-Valuet1&comma;1

40t472t3&plus;48t212t&plus;3

(7)

See Also

convert/MatrixPolynomialObject

LagrangeBasis

LinearAlgebra[CompanionMatrix]

NewtonBasis

OrthogonalSeries

PochhammerBasis

type/MatrixPolynomialObject