Tensor diagonalization means transforming a given tensor to an exactly or nearly diagonal form through multiplying the tensor by non-orthogonal invertible matrices along selected dimensions of the tensor. It has a link to an approximate joint diagonalization (AJD) of a set of matrices. In this paper, we derive (1) a new algorithm for a symmetric AJD, which is called two-sided symmetric diagonal...

This report is a rst attempt of formalizing the diagonalization proof technique. We give a strategy how to systematically construct diagonalization proofs: (i) nding an indexing relation, (ii) constructing a diagonal element, and (iii) making the implicit contradiction of the diagonal element explicit. We suggest a declarative representation of the strategy and describe how it can be realized i...

Recently tridiagonalizafion and diagonalization have been proposed as methods to speed the EM algorithm for variance component estimation in restricted maximum likelihood. These methods require approximately the same computing resources, but only if the most efficient strategies are employed. When eigenvectors are explicitly calculated in diagonalization, computing requirements more than double...

We find a large class of integral operators which allow a systematic and explicit diagonalization. These operators generalize Abel’s integral operator, for which such a diagonalization has recently been found.

Purpose – The purpose of this paper is to present a novel gradient-based iterative algorithm for the joint diagonalization of a set of real symmetric matrices. The approximate joint diagonalization of a set of matrices is an important tool for solving stochastic linear equations. As an application, reliability analysis of structures by using the stochastic finite element analysis based on the j...