The electron paramagnetic resonance parameters (g factors g‖,g⊥ and hyperfine structure constants A‖,A⊥) of PbTiO3: Cu 2+ are calculated from the complete diagonalization method and the perturbation theory method. The calculated results obtained by the complete diagonalization method are close to that obtained by the perturbation theory method, and in good agreement with the experimental values...

Simultaneous matrix diagonalization is a key subroutine in many machine learning problems, including blind source separation and parameter estimation in latent variable models. Here, we extend joint diagonalization algorithms to low-rank and asymmetric matrices and also provide extensions to the perturbation analysis of these methods. Our results allow joint diagonalization to scale to larger p...

We present a new algorithm for approximate joint diagonalization of several symmetric matrices. While it is based on the classical least squares criterion, a novel intrinsic scale constraint leads to a simple and easily parallelizable algorithm, called LSDIC (Least squares Diagonalization under an Intrinsic Constraint). Numerical simulations show that the algorithm behaves well as compared to o...

We present a new approach to approximate joint diagonalization of a set of matrices. The main advantages of our method are computational efficiency and generality. The algorithm is based on the Frobeniusnorm formulation of the joint diagonalization problem, and addresses diagonalization with a general, non-orthogonal transformation. The iterative scheme of the algorithm inherits the key ideas f...

The Kohn-Sham equation in first-principles density functional theory (DFT) calculations is a nonlinear eigenvalue problem. Solving the nonlinear eigenproblem is usually the most expensive part in DFT calculations. Sparse iterative diagonalization methods that compute explicit eigenvectors can quickly become prohibitive for large scale problems. The Chebyshevfiltered subspace iteration (CheFSI) ...

Four equivalent approaches of estimating variance components from mixed-model equations including the relationship matrix are presented. One procedure involves simultaneous diagonalization of the coefficient matrix (Z'MZ) and the inverse of the numerator relationship matrix (A-1). After simultaneous diagonalization, the absorbed coefficient matrix of the mixed-model equations is diagonal, so so...

A new efficient algorithm is presented for joint diagonalization of several matrices. The algorithm is based on the Frobenius-norm formulation of the joint diagonalization problem, and addresses diagonalization with a general, non-orthogonal transformation. The iterative scheme of the algorithm is based on a multiplicative update which ensures the invertibility of the diagonalizer. The algorith...

Diagonalization is a powerful technique in recursion theory and in computational complexity [2]. The limits of this technique are not clear. On the one hand, many people argue that conflicting relativizations mean a complexity question cannot be resolved using only diagonalization. On the other hand, it is not clear that diagonalization arguments necessarily relativize. In [5], the authors prop...