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Matrix Transposition on a Mesh with Blocking Transmissions
Parallel Processing Letters, 1998A time-optimal procedure to transpose in situ a matrix stored over a distributed memory 2-dimensional mesh-connected parallel computer is shown. The matrix need not be square. Only nearest-neighbor blocking communications is used, and a small bounded buffer space is required.
Micha Hofri, David L. Thomson
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On the Congruence Centralizers of a Block Diagonal Matrix and the Horn–Sergeichuk Matrix
Computational Mathematics and Mathematical Physics, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The Congruent Centralizer of a Block Diagonal Matrix
Journal of Mathematical Sciences, 2017Let \(A\) be a complex \(n\times n\) block diagonal matrix of the form \[ A=\left( \begin{matrix} B & 0\\ 0 & C \end{matrix} \right), \] where \(B\) and \(C\) have no common eigenvalues. Let \(X\) be an arbitrary matrix commuting with \(A.\) Then \(X\) has the same block diagonal form as the matrix \(A\).
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The Determinant of a Triangular-Block Matrix
SIAM Review, 1996Matthew Roughan, Kenneth Pope
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Hybrid 2D/1D Blocking as Optimal Matrix-Matrix Multiplication
2013Multiplication of huge matrices generates more cache misses than smaller matrices. 2D block decomposition of matrices that can be placed in L1 CPU cache decreases the cache misses since the operations will access data only stored in L1 cache. However, it also requires additional reads, writes, and operations compared to 1D partitioning, since the ...
Marjan Gusev +2 more
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Block ILU Preconditioners for a Nonsymmetric Block-Tridiagonal M-Matrix
BIT Numerical Mathematics, 2000The paper is directed to preconditioning linear equations that arise from finite difference methods or finite elements. It is assumed that the matrix elements outside of the diagonal blocks are not positive. The assumption holds for finite difference methods and for some finite element methods of lowest order. Comparison theorems for \(M\)-matrices can
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The block con-similarity of block compound matrix
2012 7th International Conference on System of Systems Engineering (SoSE), 2012null Libo Liu, null Changling Xu
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