BernsteinBasis
Bernstein polynomials on an interval
Calling Sequence
Parameters
Description
Examples
BernsteinBasis(k, n, a, b, x)
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
BernsteinBasisk,n,a,b,x=nkb−xn−kx−akb−an 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.
p≔3BernsteinBasis0,4,0,1,x+5BernsteinBasis2,4,0,1,x+7BernsteinBasis4,4,0,1,x
P≔convertp,MatrixPolynomialObject,x
P≔RecordValue=Defaultvalue,Variable=x,Degree=4,Coefficient=coe,Dimension=1,1,Basis=BernsteinBasis,BasisParameters=4,0,1,IsMonic=mon,OutputOptions=shape=,storage=rectangular,order=Fortran_order,fill=0,attributes=
P:-Degree
4
Note that the result returned by convert(...,MatrixPolynomialObject) represents a matrix polynomial; hence these results are 1 by 1 matrices.
P:-Value0
3
P:-Value1
7
P:-Value0.3
2.100000000
factorP:-Valuet1,1
40t4−72t3+48t2−12t+3
See Also
convert/MatrixPolynomialObject
LagrangeBasis
LinearAlgebra[CompanionMatrix]
NewtonBasis
OrthogonalSeries
PochhammerBasis
type/MatrixPolynomialObject
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