New Jacobi-like algorithms for non-orthogonal joint diagonalization of Hermitian matrices

• Two Jacobi-like algorithms are established under a reasonable assumption.
• The GERALD2b algorithm converges the fastest among the four algorithms.
• Convergence statistics are shown to illustrate the performances of algorithms.

In this paper, two new algorithms are proposed for non-orthogonal joint matrix diagonalization under Hermitian congruence. The idea of these two algorithms is based on the so-called Jacobi algorithm for solving the eigenvalues problem of Hermitian matrix. The algorithms are then called ‘general Jabobi-like diagonalization’ algorithms (GERALD). They are based on the search of two complex parameters by the minimization of a quadratic criterion corresponding to a measure of diagonality. Lastly, numerical simulations are conducted to illustrate the effective performances of the GERALD algorithms.