Results 31 to 40 of about 1,075 (62)

Bidiagonalization of (k, k + 1)-tridiagonal matrices

Special Matrices, 2019
In this paper,we present the bidiagonalization of n-by-n (k, k+1)-tridiagonal matriceswhen n < 2k. Moreover,we show that the determinant of an n-by-n (k, k+1)-tridiagonal matrix is the product of the diagonal elements and the eigenvalues of the matrix ...
Takahira S., Sogabe T., Usuda T.S.
doaj   +1 more source

Analysis of the singular value decomposition as a tool for processing microarray expression data [PDF]

, 2005
We give two informative derivations of a spectral algorithm for clustering and partitioning a bi-partite graph. In the first case we begin with a discrete optimization problem that relaxes into a tractable continuous analogue.
Higham, D.J., Kalna, G., Vass, J.K.
core  

Verified partial eigenvalue computations using contour integrals for Hermitian generalized eigenproblems

, 2019
We propose a verified computation method for partial eigenvalues of a Hermitian generalized eigenproblem. The block Sakurai-Sugiura Hankel method, a contour integral-type eigensolver, can reduce a given eigenproblem into a generalized eigenproblem of ...
Imakura, Akira, Morikuni, Keiichi, Takayasu, Akitoshi   +2 more
core   +1 more source

A Dimension Reduction Scheme for the Computation of Optimal Unions of Subspaces [PDF]

, 2011
Given a set of points \F in a high dimensional space, the problem of finding a union of subspaces \cup_i V_i\subset \R^N that best explains the data \F increases dramatically with the dimension of \R^N.
Aldroubi, Akram, Anastasio, Magalí, Cabrelli, Carlos, Molter, Ursula   +3 more
core   +1 more source

Eigenpairs of adjacency matrices of balanced signed graphs

Special Matrices
In this article, we study eigenvalues λ\lambda and their associated eigenvectors xx of the adjacency matrices AA of balanced signed graphs. Balanced signed graphs were first introduced and studied by Harary to handle a problem in social psychology ...
Chen Mei-Qin
doaj   +1 more source

Test matrices with specified eigenpairs for the symmetric positive definite generalized eigenvalue problem

Special Matrices
The generalized eigenvalue problem is a significant topic with numerous applications in scientific and technological computing. Therefore, verifying the reliability of the results produced by numerical solvers is crucial.
Ozaki Katsuhisa, Terao Takeshi
doaj   +1 more source

Iterative building of Barabanov norms and computation of the joint spectral radius for matrix sets

, 2010
The problem of construction of Barabanov norms for analysis of properties of the joint (generalized) spectral radius of matrix sets has been discussed in a number of publications.
Kozyakin, Victor
core   +1 more source

Geršhgorin-type theorems for Z1-eigenvalues of tensors with applications

Demonstratio Mathematica
In this article, we present several Geršhgorin-type theorems for Z1{Z}_{1}-eigenvalues of tensors, which improve the results provided by Wang et al. (Some upper bounds on Zt{Z}_{t}-eigenvalues of tensors, Appl. Math. Comput.
Shen Xiaowei, Hao Qian, He Jun, Wang Guangbin   +3 more
doaj   +1 more source

A note on the growth factor in Gaussian elimination for generalized Higham matrices

, 2013
The Higham matrix is a complex symmetric matrix A=B+iC, where both B and C are real, symmetric and positive definite and $\mathrm{i}=\sqrt{-1}$ is the imaginary unit. For any Higham matrix A, Ikramov et al.
Gu, Xian-Ming, Guo, Qian-Ping, Li, Hou-biao   +2 more
core  

On condition numbers of polynomial eigenvalue problems with nonsingular leading coefficients [PDF]

, 2008
In this paper, we investigate condition numbers of eigenvalue problems of matrix polynomials with nonsingular leading coefficients, generalizing classical results of matrix perturbation theory.
Papathanasiou, Nikolaos, Psarrakos, Panayiotis   +1 more
core   +1 more source