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The inverses of block tridiagonal matrices
Applied Mathematics and Computation, 2006Combining an LU and a UL decomposition of a block tridiagonal matrix a twisted block decomposition of the matrix and an iterative formula for the computation of the block elements of the inverse matrix are derived. Furthermore, considering only the multiplication and division operations a comparison of the computational complexity of the new algorithm ...
Ting-Zhu Huang
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Numerical Algorithms, 2013 For a class of block two-by-two systems of linear equations with certain skew-Hamiltonian coefficient matrices, we construct additive block diagonal preconditioning matrices and discuss the eigen-properties of the corresponding preconditioned matrices ...
Zeng-Qi Wang, Zhong-Zhi Bai
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Decomposing Matrices into Blocks
SIAM Journal on Optimization, 1998Summary: In this paper we investigate whether matrices arising from linear or integer programming problems can be decomposed into so-called bordered block diagonal form. More precisely, given some matrix \(A\), we try to assign as many rows as possible to some number \(\beta\) of blocks of size \(\kappa\) such that no two rows assigned to different ...
Ralf Borndörfer +2 more
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Linear and Multilinear Algebra, 1998 Elsner L, Szulc T. Block P-matrices. Linear and Multilinear Algebra.
Tomasz Szulc
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A note on “Block H-matrices and spectrum of block matrices”
Applied Mathematics and Mechanics, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liu, Jian-Zhou, Huang, Ze-Jun
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Block H-matrices and spectrum of block matrices
Applied Mathematics and Mechanics, 2002Several generalizations for block \(H\)-matrices are studied by the concept of \(G\)-functions. Equivalent characterizations of \(H\)-matrices are discussed. A spectrum location of block \(H\)-matrices is determined.
Huang, Tingzhu, Li, Wen
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On the inertia of the block H‐matrices
Numerical Linear Algebra with Applications, 2017SummaryThe problem of determining matrix inertia is very important in many applications, for example, in stability analysis of dynamical systems. In the (point‐wise) H‐matrix case, it was proven that the diagonal entries solely reveal this information. This paper generalises these results to the block H‐matrix cases for 1, 2, and matrix norms.
Kostić, Vladimir, Cvetković, Ljiljana
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Positivity of Block Tridiagonal Matrices
SIAM Journal on Matrix Analysis and Applications, 1998The authors give some results concerning the disconjugacy of linear Hamiltonian difference systems \[ \Delta x_k = A_k x_{k+1} + B_k u_k,\quad \Delta u_k = C_k x_{k+1} - A_k^T u_k \] and hence positive definiteness of the discrete quadratic functional \[ {\mathcal F}(x,u) ={\sum_{k=0}^N} \{u_k^T B_k u_k + x_{k+1}^T C_k x_{k+1}\} \] to positive ...
Martin Bohner, Ondrej Doslý
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