A New Algorithm for Complex Non-Orthogonal Joint Diagonalization Based on Shear and Givens Rotations

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Abstract
This paper introduces a new algorithm to approximate non-orthogonal joint diagonalization (NOJD) of a set of complex matrices. This algorithm is based on the Frobenius norm formulation of the joint diagonalization (JD) problem and takes advantage from combining Givens and Shear rotations to attempt the approximate JD. It represents a non-trivial generalization of the JDi (Joint Diagonalization) algorithm (Souloumiac 2009) to the complex case. The JDi is first slightly modified then generalized to the CJDi (i.e., Complex JDi) using complex to real matrix transformation. Several methods already exist in the literature. Consequently, we provide herein a brief overview of existing NOJD algorithms. Then we provide an extensive comparative study to illustrate the effectiveness and stability of the CJDi with respect to various system parameters and application contexts.
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