A Jacobi-like joint diagonalization method by one-dimensional optimization

• The Jacobi rotation matrix depends on a single parameter.
• The complex target matrices are transformed into real symmetric ones.
• Joint diagonalization can be obtained by one-dimensional optimization.
• It can handle the complex matrices by modifying algorithm implementation.
• The proposed algorithms have the good performance like the SOBI algorithm.

We present an improved version of the famous orthogonal joint diagonalization (JD) of a set of matrices, on the basis of successive Jacobi-like transformations. In particular, the Jacobi transformation matrix in each rotation step is only dependent on a single parameter that has analytical solution in real-value case. If this algorithm is improved, it can indirectly deal with the complex target matrices that can be converted into real symmetric ones. Moreover, this algorithm can be modified to handle the complex target matrices by a bi-Givens rotation procedure. The overall algorithm performance is evaluated through numerical simulations, and compared favorably with some existing state-of-the-art methods in terms of speed of convergence, complexity and accuracy.