LagrangeBasis
Lagrange polynomials on a set of nodes
Calling Sequence
Parameters
Description
Examples
LagrangeBasis(k, nodes, x)
k
-
algebraic expression; the index
nodes
list of algebraic expressions; the nodes where the polynomial is known
x
algebraic expression; the argument
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.
That polynomial has the value 3 at , the value 0 at , the value 5 at , and the value 7 at .
Note that the result returned by represents a matrix polynomial; hence these results are 1 by 1 matrices.
See Also
BernsteinBasis
convert/MatrixPolynomialObject
LinearAlgebra[CompanionMatrix]
NewtonBasis
OrthogonalSeries
PochhammerBasis
type/MatrixPolynomialObject
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