Contains a suite for approximating the solution of a parameterized matrix equation using either a residual minimizing spectral Galerkin method or pseudospectral method. Both methods employ a basis of orthogonal polynomials -- multivariate polynomials are constructed at products of univariate polynomials.
Demos are provided, although the demo for solving the elliptic PDE with a Karhunen-Loeve expansion for the log of the coefficients requires the MATLAB PDE Toolbox.
Also contains utilities for working with the orthogonal polynomials and associated Gaussian quadrature rules.
Ok, from the code I understood that the computed polynomials (Legendre, Chebyshev, Jacobi etc.) are in fact orthonormal and not only orthogonal w.r.t. a certain weight.
So were the legendre polynomials constructed using the uniform weight of 0.5 and chebyshev with 1/pi*(1-x^2)^-0.5? How can we extract the resulting polynomial coefficients?
The Legendre polynomials should assume fixed values at the points x = -1 and x = 1. However, when I plot them using the evaluate_expansion function I see that this is not the case. Is this a bug?
Inspired by: Random Field Simulation