Results 21 to 30 of about 155 (114)

A note on certain ergodicity coeflcients

Special Matrices, 2015
We investigate two ergodicity coefficients ɸ ∥∥ and τn−1, originally introduced to bound the subdominant eigenvalues of nonnegative matrices. The former has been generalized to complex matrices in recent years and several properties for such generalized ...
Tudisco Francesco
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The smallest singular value anomaly: The reasons behind sharp anomaly

Special Matrices
Let AA be an arbitrary matrix in which the number of rows, mm, is considerably larger than the number of columns, nn. Let the submatrix Ai,i=1,…,m{A}_{i},\hspace{0.33em}i=1,\ldots ,m, be composed from the first ii rows of AA, and let βi{\beta }_{i ...
Dax Achiya
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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.
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Block diagonalization of (p, q)-tridiagonal matrices

Special Matrices
In this article, we study the block diagonalization of (p,q)\left(p,q)-tridiagonal matrices and derive closed-form expressions for the number and structure of diagonal blocks as functions of the parameters pp, qq, and nn. This reduction enables efficient
Manjunath Hariprasad
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Solving an Elliptic PDE Eigenvalue Problem via Automated Multi-Level Substructuring and Hierarchical Matrices [PDF]

, 2020
We propose a new method for the solution of discretised elliptic PDE eigenvalue problems. The new method combines ideas of domain decomposition, as in the automated multi-level substructuring (short AMLS), with the concept of hierarchical matrices (short
Lars Grasedyck, Peter Gerds
core  

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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Alternating direction method for bi-quadratic programming

Alternating direction method, Bi-quadratic programming, Quadratic semidefinite programming, 65F15, 65K05, 90C90,
Sheng-Long Hu, Zheng-Hai Huang
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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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Forecasting with unequally spaced data by a functional principal component approach

Karhunen-Loève expansion, least-squares linear prediction, orthogonal projection, principal components, 60G25, 60G12, 65F15,
Francisco Ocaña, Mariano Valderrama, Ana Aguilera   +2 more
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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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