On fast multiplication of a matrix by its transpose [PDF]
, 2020 We present a non-commutative algorithm for the multiplication of a 2x2-block-matrix by its transpose using 5 block products (3 recursive calls and 2 general products) over C or any finite field.We use geometric considerations on the space of bilinear ...
Dumas, Jean-Guillaume +2 more
core +3 more sources
The power of block-encoded matrix powers: improved regression techniques via faster Hamiltonian simulation [PDF]
International Colloquium on Automata, Languages and Programming, 2018 We apply the framework of block-encodings, introduced by Low and Chuang (under the name standard-form), to the study of quantum machine learning algorithms and derive general results that are applicable to a variety of input models, including sparse ...
Shantanav Chakraborty +2 more
semanticscholar +1 more source
Miscellaneous equalities for idempotent matrices with applications
Open Mathematics, 2020 This article brings together miscellaneous formulas and facts on matrix expressions that are composed by idempotent matrices in one place with cogent introduction and references for further study.
Tian Yongge
doaj +1 more source
Characterizations of the group invertibility of a matrix revisited
Demonstratio Mathematica, 2022 A square complex matrix AA is said to be group invertible if there exists a matrix XX such that AXA=AAXA=A, XAX=XXAX=X, and AX=XAAX=XA hold, and such a matrix XX is called the group inverse of AA.
Tian Yongge
doaj +1 more source
Experimental and modeling study on the effect of molecular diffusion during CO2 injection
Petroleum Research, 2021 In this work, a new approach based on the effect of molecular diffusion on oil recovery during CO2 injection in naturally fractured reservoirs has been proposed to examine the best condition for oil recovery in the matrix block.
Vahid Moayedi Esfahani +3 more
doaj +1 more source
Real block-circulant matrices and DCT-DST algorithm for transformer neural network
Frontiers in Applied Mathematics and Statistics, 2023 In the encoding and decoding process of transformer neural networks, a weight matrix-vector multiplication occurs in each multihead attention and feed forward sublayer.
Euis Asriani +4 more
doaj +1 more source
Photonic matrix multiplication lights up photonic accelerator and beyond
Light: Science & Applications, 2022 Matrix computation, as a fundamental building block of information processing in science and technology, contributes most of the computational overheads in modern signal processing and artificial intelligence algorithms.
Hailong Zhou +11 more
semanticscholar +1 more source
Identities and exponential bounds for transfer matrices [PDF]
, 2012 This paper is about analytic properties of single transfer matrices originating from general block-tridiagonal or banded matrices. Such matrices occur in various applications in physics and numerical analysis.
Molinari, Luca G
core +2 more sources
Algorithms for simultaneous block triangularization and block diagonalization of sets of matrices
AIMS Mathematics, 2023 In a recent paper, a new method was proposed to find the common invariant subspaces of a set of matrices. This paper investigates the more general problem of putting a set of matrices into block triangular or block-diagonal form simultaneously.
Ahmad Y. Al-Dweik +3 more
doaj +1 more source
A Novel Partitioning Method for Accelerating the Block Cimmino Algorithm [PDF]
, 2018 We propose a novel block-row partitioning method in order to improve the convergence rate of the block Cimmino algorithm for solving general sparse linear systems of equations.
Aykanat, Cevdet +2 more
core +2 more sources