Numerical Efficiency of Block-diagonalization Method

Numerical block diagonalization of matrix *-algebras with application to semidefinite programming

Semidefinite programming (SDP) is one of the most active areas in mathematical programming, due to varied applications and the availability of interior point algorithms. In this paper we propose a new pre-processing technique for SDP instances that exhibit algebraic symmetry. We present computational results to show that the solution times of certain SDP instances may be greatly reduced via the...

Block Diagonalization of Nearly Diagonal Matrices

In this paper we study the effect of block diagonalization of a nearly diagonal matrix by iterating the related Riccati equations. We show that the iteration is fast, if a matrix is diagonally dominant or scaled diagonally dominant and the block partition follows an appropriately defined spectral gap. We also show that both kinds of diagonal dominance are not destroyed after the block diagonali...

Fast block diagonalization of k-tridiagonal matrices

In the present paper, we give a fast algorithm for block diagonalization of k-tridiagonal matrices. The block diagonalization provides us with some useful results: e.g., another derivation of a very recent result on generalized k-Fibonacci numbers in [M.E.A. El-Mikkawy, T. Sogabe, A new family of k-Fibonacci numbers, Appl. Math. Comput. 215 (2010) 4456– 4461]; efficient (symbolic) algorithm for...

Random Matrix Diagonalization—Some Numerical Computations

A flexible method of creating HMM using block-diagonalization of covariance matrices

A new algorithm to reduce the amount of calculation in the likelihood computation of continuous mixture HMM(CMHMM) with block-diagonal covariance matrices while retaining high recognition rate is proposed. The block matrices are optimized by minimizing di erence between the output probability calculated with full covariance matrices and that calculated with block-diagonal covariance matrices. T...