Simultaneous Diagonalization With Similarity Transformation for Non-Defective Matrices

The problem of joint eigenstructure estimation for the non-defective matrices is addressed. A procedure revealing the joint eigenstructure by simultaneous diagonalization with unitary and non-unitary similarity transformations alternately is proposed to overcome the convergence difficulties of previous methods based on simultaneous Schur form and unitary transformations. It can be proved that its asymptotic convergence rate is ultimately quadratic. Numerical experiments are conducted in a multi-dimensional harmonic retrieval application and suggest that the method presented here converges considerably faster than the methods based on only unitary transformation for matrices which are not near to normality