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LagrangeBasis - Lagrange polynomials on a set of nodes
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
LagrangeBasis(k,nodes,x) = w[k]*prod(x-nodes[j], j<>k) 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 and subsequent call to , which uses the numerically stable barycentric form to evaluate the polynomial .
Examples
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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