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## PMPack - Parameterized Matrix Package

version 1.0.0.0 (686 KB) by
Polynomial spectral methods for solving parameterized matrix equations.

Updated 01 Nov 2010

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.

### Cite As

Paul Constantine (2021). PMPack - Parameterized Matrix Package (https://www.mathworks.com/matlabcentral/fileexchange/29228-pmpack-parameterized-matrix-package), MATLAB Central File Exchange. Retrieved .

haisong zhao

Sava Marinkov

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?

Sava Marinkov

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?

João

##### MATLAB Release Compatibility
Created with R2009b
Compatible with any release
##### Platform Compatibility
Windows macOS Linux
##### Acknowledgements

Inspired by: Random Field Simulation

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