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Numerical study of the mechanical behaviour of unwelded block in matrix rocks under direct shearing
Bulletin of Engineering Geology and the Environment, 2023A. Sheikhpourkhani +3 more
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Computational Science & Discovery, 2012
We present an algorithm for computing any block of the inverse of a block tridiagonal, nearly block Toeplitz matrix (defined as a block tridiagonal matrix with a small number of deviations from the purely block Toeplitz structure). By exploiting both the block tridiagonal and the nearly block Toeplitz structures, this method scales independently of the
Matthew G Reuter, Judith C Hill
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We present an algorithm for computing any block of the inverse of a block tridiagonal, nearly block Toeplitz matrix (defined as a block tridiagonal matrix with a small number of deviations from the purely block Toeplitz structure). By exploiting both the block tridiagonal and the nearly block Toeplitz structures, this method scales independently of the
Matthew G Reuter, Judith C Hill
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Block-Equations and Matrix-Inversion
1983An “ordinary” system of linear equations can be formulated in matrix notation, as follows: $$ {\rm{A}} \cdot \underline {\rm{x}} = \underline {\rm{b}} $$
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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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Parallel Performance of Block ILU Preconditioners for a Block-tridiagonal Matrix
The Journal of Supercomputing, 2003The parallel implementation for Krylov subspace methods of the block ILU preconditioners for block-tridiagonal matrices proposed by the author [BIT 40, 583-605 (2000; Zbl 0961.65040)] is discussed. Especially an efficient implementation for a five-point discretisation of an elliptic second-order partial differential equation is discussed, and more ...
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The biofilm matrix: multitasking in a shared space
Nature Reviews Microbiology, 2022Hans-Curt Flemming +2 more
exaly
The generalized Drazin inverse of a block matrix in a Banach algebra
Aequationes Mathematicae, 2013D. Mosić, D. Djordjevic
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