NewtonBasis - Maple Help
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NewtonBasis

Newton polynomials on a set of nodes

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

NewtonBasis(k, nodes, x)

Parameters

k

-

algebraic expression; the index

nodes

-

list of algebraic expressions; nodes where the polynomial is known

x

-

algebraic expression; the argument

Description

• 

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 .

Examples

(1)

(2)

The coefficients of that polynomial can be interpreted in terms of divided differences of the values of  at the nodes.

(3)

(4)

Note that the result returned by  represents a matrix polynomial; hence these results are 1 by 1 matrices.

(5)

(6)

(7)

See Also

BernsteinBasis

convert/MatrixPolynomialObject

LagrangeBasis

LinearAlgebra[CompanionMatrix]

OrthogonalSeries

PochhammerBasis

type/MatrixPolynomialObject

 


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