Block Jacobi-type methods for non-orthogonal joint diagonalisation

In this paper, we study the problem of non-orthogonal joint diagonalisation of a set of real symmetric matrices. A family of block Jacobitype methods are proposed to optimise two popular cost functions for the non-orthogonal joint diagonalisation, namely, the off-norm function and the log-likelihood function. By exploiting the appropriate underlying manifold, namely the so-called oblique manifold, rigorous analysis shows that, under the exact non-orthogonal joint diagonalisation setting, the proposed methods converge locally quadratically fast to a joint diagonaliser. Finally, performance of our methods is investigated by numerical experiments for both exact and approximate non-orthogonal joint diagonalisation.

• Type: Conference
• Year: 2009
• Where: ICASSP
• Authors: Hao Shen, Knut Hüper
• Keywords: Block Jacobitype Methods, ICASSP 2009, Non-orthogonal Joint Diagonalisation, Real Symmetric Matrices, Signal Processing