The eigenvalue distribution of block diagonally dominant matrices and block H-matrices.
Zhang, Cheng-Yi, Luo, Shuanghua, Huang, Aiqun, Xu, Chengxian (2010)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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Displaying similar documents to “The estimates of diagonally dominant degree and eigenvalues inclusion regions for the Schur complement of block diagonally dominant matrices”
The eigenvalue distribution of block diagonally dominant matrices and block H-matrices.
Simultaneous triangularization of commuting matrices for the solution of polynomial equations
Vanesa Cortés, Juan Peña, Tomas Sauer (2012)
Open Mathematics
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We present an extension of the QR method to simultaneously compute the joint eigenvalues of a finite family of commuting matrices. The problem is motivated by the task of finding solutions of a polynomial system. Several examples are included.
Schur complements of diagonally dominant matrices
David Carlson, Thomas L. Markham (1979)
Czechoslovak Mathematical Journal
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Existence of matrices with prescribed entries.
Ion Zaballa (1986)
Extracta Mathematicae
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A note on certain ergodicity coeflcients
Francesco Tudisco (2015)
Special Matrices
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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 version have been shown so far.We provide a further result concerning the limit of its powers. Then we propose a generalization of the second coefficient τ n−1 and we show that, under mild conditions, it can be used to recast the eigenvector...
A note on nonnegative matrices
Miroslav Fiedler (1977)
Mathematica Slovaca
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Certain new M-matrices and their properties with applications
Ratnakaram N. Mohan, Sanpei Kageyama, Moon H. Lee, G. Yang (2008)
Discussiones Mathematicae Probability and Statistics
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The Mₙ-matrix was defined by Mohan [21] who has shown a method of constructing (1,-1)-matrices and studied some of their properties. The (1,-1)-matrices were constructed and studied by Cohn [6], Ehrlich [9], Ehrlich and Zeller [10], and Wang [34]. But in this paper, while giving some resemblances of this matrix with a Hadamard matrix, and by naming it as an M-matrix, we show how to construct partially balanced incomplete block designs and some regular graphs by it. Two types of these...
Block distance matrices.
Balaji, R., Bapat, R.B. (2007)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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Eigenvalues and eigenvectors of some tridiagonal matrices with non-constant diagonal entries
S. Kouachi (2008)
Applicationes Mathematicae
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We give explicit expressions for the eigenvalues and eigenvectors of some tridiagonal matrices with non-constant diagonal entries. Our techniques are based on the theory of recurrent sequences.
Condition numbers of Hessenberg companion matrices
Michael Cox, Kevin N. Vander Meulen, Adam Van Tuyl, Joseph Voskamp (2024)
Czechoslovak Mathematical Journal
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The Fiedler matrices are a large class of companion matrices that include the well-known Frobenius companion matrix. The Fiedler matrices are part of a larger class of companion matrices that can be characterized by a Hessenberg form. We demonstrate that the Hessenberg form of the Fiedler companion matrices provides a straight-forward way to compare the condition numbers of these matrices. We also show that there are other companion matrices which can provide a much smaller condition...
A new block triangular preconditioner for three-by-three block saddle-point problem
Jun Li, Xiangtuan Xiong (2024)
Applications of Mathematics
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In this paper, to solve the three-by-three block saddle-point problem, a new block triangular (NBT) preconditioner is established, which can effectively avoid the solving difficulty that the coefficient matrices of linear subsystems are Schur complement matrices when the block preconditioner is applied to the Krylov subspace method. Theoretical analysis shows that the iteration method produced by the NBT preconditioner is unconditionally convergent. Besides, some spectral properties...