computeGauss.m

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computeGauss.m#

Compute the Gaussian rule corresponding to the orthogonal polynomials that are defined by the coefficients alpha and beta, according to the three-term recurrence relation for orthogonal polynomials:

\[ p_i(x) = (x-\alpha_i) p_{i-1}(x) - \beta_i p_{i-2}(x), \]

for \(i=1\ldots,N\), with

\[ p_0(x) = 1, \text{ and } p_0(x) = 0. \]
[x,w] = computeGauss(N, alpha, beta)

For more information, see [Gautschi, 2004].

Inputs#

  • N : The number of points for the quadrature rule.

  • alpha and beta : Recurrence coefficients.

Outputs#

  • x : Array of quadrature points

  • w : Array of quadrature weights.

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