Some Papers and Codes on Joint Diagonalization
In this page you can find:
- Code and paper on a set of simple algorithms for non-orthogonal matrix joint diagonalization
- Two papers concerning the issue of sensitivity of the problem of matrix joint diagonalization
Four algorithms LUJ1D, QRJ1D, LUJ2D and QRJ2D are simple algorithms for non-orthogonal joint
diagonalization of a set of symmetric matrices. They are based on the idea of extension of the application
of Jacobi matrices (rotations) to non-orthogonal groups and successive one-dimensional optimization using these matrices.
- Bijan Afsari, ``Simple LU and QR Based Non-orthogonal Matrix Joint Diagonalization,'' ICA 2006,
Springer LNCS 3889, pp.1-7, 2006, [paper.pdf], [slide(ps)]
- Matlab codes: LUJ1D, QRJ1D, LUJ2D, QRJ2D, All codes zipped
An interesting issue related to the problem of non-orthogonal joint diagonalization is the question:``what
affects the sensitivity of the problem or what is the condition number that can be associated to this problem?''. This question has been addressed in the following two papers:
- Bijan Afsari, ``What Can Make Joint Diagonalization Difficult?,'' Proc. of ICASSP2007, April 2007,
[.pdf]
- Bijan Afsari,``Sensitivity Analysis for the Problem of Matrix Joint Diagonalization,'' accepted, SIAM Journal on Matrix Analysis (Special issue on tensorial methods) [.pdf]
- A related talk: [.ps][.pdf]
Page Maintained By:Bijan Afsari
Last Modified: Feb, 26, 2007