LagrangeBasis - Maple Help
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LagrangeBasis

Lagrange polynomials on a set of nodes

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

LagrangeBasis(k, nodes, x)

Parameters

k

-

algebraic expression; the index

nodes

-

list of algebraic expressions; the nodes where the polynomial is known

x

-

algebraic expression; the argument

Description

• 

 defines the th Lagrange polynomial of degree  which is either  or  on the given nodes. By convention, the nodes are indexed from , so  , and the barycentric weights  are defined as .

• 

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 numerically stable barycentric form to evaluate the polynomial p.

Examples

(1)

(2)

That polynomial has the value 3 at , the value 0 at , the value 5 at , and the value 7 at .

(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

LinearAlgebra[CompanionMatrix]

NewtonBasis

OrthogonalSeries

PochhammerBasis

type/MatrixPolynomialObject

 


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