NewtonBasis
Newton polynomials on a set of nodes
Calling Sequence
Parameters
Description
Examples
NewtonBasis(k, nodes, x)
k
-
algebraic expression; the index
nodes
list of algebraic expressions; nodes where the polynomial is known
x
algebraic expression; the argument
The th Newton polynomial of degree is defined by
By convention, the nodes are indexed from , so .
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 Horner's method to evaluate the polynomial .
The coefficients of that polynomial can be interpreted in terms of divided differences of the values of at the nodes.
Note that the result returned by represents a matrix polynomial; hence these results are 1 by 1 matrices.
See Also
BernsteinBasis
convert/MatrixPolynomialObject
LagrangeBasis
LinearAlgebra[CompanionMatrix]
OrthogonalSeries
PochhammerBasis
type/MatrixPolynomialObject
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