Simple LU and QR based non-orthogonal matrix joint diagonalization

A class of simple Jacobi-type algorithms for non-orthogonal matrix joint diagonalization based on the LU or QR factorization is introduced. By appropriate parametrization of the underlying manifolds, i.e. using triangular and orthogonal Jacobi matrices we replace a high dimensional minimization problem by a sequence of simple one dimensional minimization problems. In addition, a new scale-invariant cost function for non-orthogonal joint diagonalization is employed. These algorithms are step-size free. Numerical simulations demonstrate the efficiency of the methods.