Class OPoly

Inheritance Relationships

Base Type

  • public handle

Class Documentation

class OPoly : public handle

Class storing and managin orthogonal polynomial

Public Functions

function OPoly(varargin)
function eval(n,x)

Evaluate the polynomial \( p_n(x) \) where \( n \) is the degree of the polynomial. The value \( x \) can be a scalar a vector or a matrix. The result is of the same dimension of \( x \).

function eval2(n,x)

Evaluate the polynomial \( p_n(x) \) and \( p'_n(x) \) where \( n \) is the degree of the polynomial. Moreover a sign variation of the Sturm sequence associated to the recurrence is returned. The value \( x \) can be a scalar a vector or a matrix. The results are of the same dimension of \( x \).

function sequence(n,x)

Evaluate the sequence \( p_0(x), p_1(x),\ldots, p_n(x) \). Moreover a sign variation of the Sturm sequence associated to the recurrence is returned. The value \( x \) can be a scalar a vector or a matrix. The results are of the same dimension of \( x \).

If x is an m x p matrix then PP is an array of dimension n x m x p

function zeros(n,epsi)

Evaluate all the zeros of the orthogonal polynomial \( p_n(x) \).

  • n is the degree of the polynomial

  • epsi is the tolerance used in the computation of the zeros

function gauss(n,epsi)

Evaluate all nodes and weight of the Gauss-Legendre quadrature. The nodes are the zeros of the associated Legendre polynomial

  • n is the number of interpolation point

  • epsi is the tolerance used in the computation of the zeros of the orthogonal polynomial