A least-squares approach to joint Schur decomposition

We address the problem of joint Schur decomposition (JSD) of several matrices. This problem is of great importance for many signal processing applications such as sonar, biomedicine, and mobile communications. We rst present a least-squares (LS) approach for computing the JSD. The LS approach is shown to coincide with that proposed intuitively by Haardt et al, thus establishing the optimality of their criterion in the least-squares sense. Following the LS criterion, we then propose new Jacobi-like algorithms that extend and improve the existing JSD algorithms. An application of the new JSD algorithms to multidimensional harmonic retrieval is also presented.