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### Highlights from PMPack - Parameterized Matrix Package

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# PMPack - Parameterized Matrix Package

### Paul Constantine (view profile)

Polynomial spectral methods for solving parameterized matrix equations.

File Information
Description

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.

Acknowledgements

Random Field Simulation inspired this file.

MATLAB release MATLAB 7.9 (R2009b)
Other requirements One of the demos requires the Partial Differential Equations Toolbox.
05 Sep 2013 Sava Marinkov

### Sava Marinkov (view profile)

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?

Comment only
05 Sep 2013 Sava Marinkov

### Sava Marinkov (view profile)

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?

16 Sep 2011 João