Results 31 to 40 of about 1,108 (78)

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

On the Convergence of the Self-Consistent Field Iteration in Kohn-Sham Density Functional Theory

, 2013
It is well known that the self-consistent field (SCF) iteration for solving the Kohn-Sham (KS) equation often fails to converge, yet there is no clear explanation.
Liu, Xin, Wang, Xiao, Wen, Zaiwen, Yuan, Yaxiang   +3 more
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On the Approximation of Laplacian Eigenvalues in Graph Disaggregation

, 2016
Graph disaggregation is a technique used to address the high cost of computation for power law graphs on parallel processors. The few high-degree vertices are broken into multiple small-degree vertices, in order to allow for more efficient computation in
Hu, Xiaozhe, Urschel, John C., Zikatanov, Ludmil T.   +2 more
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A relaxation scheme for computation of the joint spectral radius of matrix sets

, 2009
The problem of computation of the joint (generalized) spectral radius of matrix sets has been discussed in a number of publications. In the paper an iteration procedure is considered that allows to build numerically Barabanov norms for the irreducible ...
Barabanov N.E., Barabanov N.E., Barabanov N.E., Kozyakin V., Kozyakin V.S., Kozyakin V.S., Protasov V.Yu., Rota G.-C., Victor Kozyakin   +8 more
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Trilogy on Computing Maximal Eigenpair

, 2017
The eigenpair here means the twins consist of eigenvalue and its eigenvector. This paper introduces the three steps of our study on computing the maximal eigenpair.
AN Langville, D Noutsos, GH Golub, J Solomon, MF Chen, MF Chen, MF Chen   +6 more
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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
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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
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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
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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
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On the condition numbers of a multiple generalized eigenvalue

, 2010
For standard eigenvalue problems, a closed-form expression for the condition numbers of a multiple eigenvalue is known. In particular, they are uniformly 1 in the Hermitian case, and generally take different values in the non-Hermitian case.
Nakatsukasa, Yuji
core