Results 131 to 140 of about 412,590 (166)
Some of the next articles are maybe not open access.
The inverse of a block-circulant matrix
IEEE Transactions on Antennas and Propagation, 1983The inverse A^{-1} of a block-circulant matrix (BCM) A is given in a closed form, by using the fact that a BCM is a combination of permutation matrices, whose eigenvalues and eigenvectors are found with the help of the complex roots of unity. Special results are also given when A is block symmetric or symmetric.
De Mazancourt, T., Gerlic, D.
openaire +2 more sources
Inverse Spectrum Problems for Block Jacobi Matrix
1993A spectrum function for the block Jacobi matrix is defined which allows to determine conditions for existence and uniqueness for the corresponding inverse spectrum problem. Two numerical algorithms for solving the inverse spectrum problem are proposed and their behaviour is illustrated on several examples of order up to 15.
Zhu, Benren +2 more
openaire +2 more sources
Random block matrix density and SS-Law
Random Operators and Stochastic Equations, 2000The author studies the symmetric random block matrices \(\Xi_{pq\times pq}=\{\delta_{ij}A_{q\times q}+ {1\over\sqrt{p}} \Xi_{q\times q}^{(ij)}\}_{i,j=1}^{p}\), where \(\delta_{ij}\) is a Kronecker symbol, \(A_{q\times q}\) are nonrandom matrices, \(\|A_{q\times q}\|\leq ...
openaire +2 more sources
Matrix Measures and Random Walks with a Block Tridiagonal Transition Matrix
SIAM Journal on Matrix Analysis and Applications, 2007Summary: We study the connection between matrix measures and random walks with a block tridiagonal transition matrix. We derive sufficient conditions such that the blocks of the \(n\)-step block tridiagonal transition matrix of the Markov chain can be represented as integrals with respect to a matrix valued spectral measure.
Dette, Holger +3 more
openaire +2 more sources
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
openaire +1 more source
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
openaire +1 more source
Block-Equations and Matrix-Inversion
1983An “ordinary” system of linear equations can be formulated in matrix notation, as follows: $$ {\rm{A}} \cdot \underline {\rm{x}} = \underline {\rm{b}} $$
openaire +1 more source
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
openaire +1 more source
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 ...
openaire +1 more source
The biofilm matrix: multitasking in a shared space
Nature Reviews Microbiology, 2022Hans-Curt Flemming +2 more
exaly