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## [Help-gsl] inverting a symmetric positive definite matrix

**From**: |
Chenyang Wang |

**Subject**: |
[Help-gsl] inverting a symmetric positive definite matrix |

**Date**: |
Mon, 23 Jan 2006 10:48:07 -0500 |

Dear Sir or mam,
I was using the gsl library to do some symmetric positive definite matrix
inversion task. I tried a few methods:
1. find the eigensystem of the symmetric positive definite matrix, then
invert the eigenvalue matrix.
result: takes 25 seconds to invert a 800x800 symmetric positive definite
matrix
2. use the gsl_linalg_LU_decomp and then gsl_linalg_LU_invert.
result: takes 6 seconds to invert a 800x800 symmetric positive definite
matrix
3. use gsl_linalg_cholesky_decomp and then loop all the columns and do
gsl_linalg_cholesky_solve to solve Ax=b. here, A is the matrix that needs to
be inverted, and b is vector in forms like: (1,0,0,0)' , (0,0,1,0)' etc,
being each column of an identity matrix.
result: takes 2 seconds to invert a 800x800 symmetric positive definite
matrix
Looks like using cholesky method is the fastest.
My question is: is there any faster way to invert a symmetric positive
definite matrix? the cholesky method looks good, but it did not take
advantage of the fact that the inverse of a symmetric matrix is also a
symmetric matrix. I think since many of the matrix inversions in real life
is done on symmetric positive definite matrix, it definitly helps to make a
function that inverts a symmetric positive definite matrix.
Thanks a lot!
Chenyang

**[Help-gsl] inverting a symmetric positive definite matrix**,
*Chenyang Wang* **<=**