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BernsteinBasis - Bernstein polynomials on an interval
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Calling Sequence
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BernsteinBasis(k, n, a, b, x)
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Parameters
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k
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algebraic expression; the index
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n
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algebraic expression; the degree
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a
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algebraic expression; left end of interval
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b
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algebraic expression; right end of interval
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x
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algebraic expression; the argument
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Description
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BernsteinBasis(k,n,a,b,x) defines the kth Bernstein polynomial of degree n which is nonnegative on the interval [a,b]. The definition is
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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.
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Examples
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![P := Record(Value = Default[value], 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 = []])](/support/helpjp/helpview.aspx?si=8525/file00012/math121.png)
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Note that the result returned by convert(...,MatrixPolynomialObject) represents a matrix polynomial; hence these results are 1 by 1 matrices.
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![Matrix([[3]])](/support/helpjp/helpview.aspx?si=8525/file00012/math139.png)
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![Matrix([[7]])](/support/helpjp/helpview.aspx?si=8525/file00012/math146.png)
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![Matrix([[2.100000000]])](/support/helpjp/helpview.aspx?si=8525/file00012/math153.png)
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![factor(P:-Value(t)[1, 1])](/support/helpjp/helpview.aspx?si=8525/file00012/math157.png)
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| (7) |
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