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## Polynomial chaos approximation

version 1.0.0.0 (8.84 KB) by Felipe Uribe

### Felipe Uribe (view profile)

Several 1D probability distributions are approximated using the polynomial chaos expansion method

Updated 12 Jun 2015

The main file 'PC_examples_1D.m' contains basic examples, in which several probability distributions are approximated using the polynomial chaos (PC) expansion. The key components of this method lie in the calculation of the orthogonal polynomials and the computation of the PC coefficients:
i). Functions to compute N-dimensional Hermite, Charlier and Jacobi polynomial are provided; extension to other types of orthogonal polynomials is straightforward.
ii). The PC coefficients are estimated using the projection method, where the integral is solved using a Gauss-Hermite quadrature. This step was only programmed for the case of 1D Hermite polynomials. Therefore, further extension to other types of orthogonal polynomials is required. An implementation of the regression method for the estimation of the PC coefficients can deal with this problem (hopefully, it will be included in a future version).

Oussama GASSAB

### Oussama GASSAB (view profile)

thank you so much, it is very useful. I would like to ask you, do you have a file that generates Legendre polynomials? (legendre_PC.m)

haisong zhao

Tianmou Liu

### Tianmou Liu (view profile)

Very helpful to the beginner of PCE. Same Error message on line 84. Replace sym2poly(PsiPol{k}) as double(sym2poly(PsiPol{k}) and executed normally. Thank you very much.

Putika Ashfar

marc rocas

yijun xu

cheung

Tathagata Roy

### Tathagata Roy (view profile)

Error in line 84. Undefined function or method 'sym2poly' for input arguments of type 'double'

yuanke

### yuanke (view profile)

george veropoulos

### george veropoulos (view profile)

Hi good work thera an explanation fo filles tnank you

Allen Zhu

### Allen Zhu (view profile)

Hi
i 'm confused about the equation in line 84 of ‘PC_examples_1D.m', and cannot find the original equation in the corresponding reference you gave. Would you please name another reference that is more accurate and easy to understand?
Thank you!

Allen Zhu

### Allen Zhu (view profile)

very helpful to the beginner of PCE

##### MATLAB Release Compatibility
Created with R2014a
Compatible with any release
##### Platform Compatibility
Windows macOS Linux