Results 11 to 20 of about 665,812 (269)
DECODING OF MATRIX-PRODUCT CODES [PDF]
Journal of Algebra and Its Applications, 2013 We propose a decoding algorithm for the (u | u + v)-construction that decodes up to half of the minimum distance of the linear code. We extend this algorithm for a class of matrix-product codes in two different ways. In some cases, one can decode beyond the error-correction capability of the code.
Hernando, Fernando, Ruano Benito, Diego
openaire +2 more sources
Matrix product state representations [PDF]
Quantum Information and Computation, 2007 This work gives a detailed investigation of matrix product state (MPS) representations for pure multipartite quantum states. We determine the freedom in representations with and without translation symmetry, derive respective canonical forms and provide efficient methods for obtaining them. Results on frustration free Hamiltonians and the generation of
Perez-Garcia, D +3 more
openaire +6 more sources
Efficiently Correcting Matrix Products [PDF]
Algorithmica, 2016 We study the problem of efficiently correcting an erroneous product of two $n\times n$ matrices over a ring. Among other things, we provide a randomized algorithm for correcting a matrix product with at most $k$ erroneous entries running in $\tilde{O}(n^2+kn)$ time and a deterministic $\tilde{O}(kn^2)$-time algorithm for this problem (where the ...
Leszek Gasieniec +4 more
openaire +8 more sources
Quantum verification of matrix products [PDF]
Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm - SODA '06, 2006 15 pages, submitted; v2: rewritten, clarified, and fixed some ...
Buhrman, H.M., Spalek, R.
openaire +5 more sources
Journal of Inequalities and Applications, 2016 A complex matrix X is called an { i , … , j } $\{i,\ldots, j\}$ -inverse of the complex matrix A, denoted by A ( i , … , j ) $A^{(i,\ldots, j)}$ , if it satisfies the ith, …, jth equations of the four matrix equations (i) A X A = A $AXA = A$ , (ii) X A X
Yongge Tian
doaj +1 more source
Stochastic Matrix Product States [PDF]
Physical Review Letters, 2010 The concept of stochastic matrix product states is introduced and a natural form for the states is derived. This allows to define the analogue of Schmidt coefficients for steady states of non-equilibrium stochastic processes. We discuss a new measure for correlations which is analogous to the entanglement entropy, the entropy cost $S_C$, and show that ...
Kristan Temme, Frank Verstraete
openaire +5 more sources
Parallel Algorithms for Masked Sparse Matrix-Matrix Products
Proceedings of the 51st International Conference on Parallel Processing, 2022 Computing the product of two sparse matrices (SpGEMM) is a fundamental operation in various combinatorial and graph algorithms as well as various bioinformatics and data analytics applications for computing inner-product similarities. For an important class of algorithms, only a subset of the output entries are needed, and the resulting operation is ...
Srdan Milakovic +4 more
openaire +2 more sources
Structured matrix recovery from matrix‐vector products
Numerical Linear Algebra with Applications, 2023 AbstractCan one recover a matrix efficiently from only matrix‐vector products? If so, how many are needed? This article describes algorithms to recover matrices with known structures, such as tridiagonal, Toeplitz, Toeplitz‐like, and hierarchical low‐rank, from matrix‐vector products.
Diana Halikias, Alex Townsend
openaire +3 more sources
Residual matrix product state for machine learning
SciPost Physics, 2023 Tensor network, which originates from quantum physics, is emerging as an efficient tool for classical and quantum machine learning. Nevertheless, there still exists a considerable accuracy gap between tensor network and the sophisticated neural network ...
Ye-Ming Meng, Jing Zhang, Peng Zhang, Chao Gao, Shi-Ju Ran
doaj +1 more source
The Forward Order Law for Least Squareg-Inverse of Multiple Matrix Products
Mathematics, 2019 The generalized inverse has many important applications in the aspects of the theoretic research of matrices and statistics. One of the core problems of the generalized inverse is finding the necessary and sufficient conditions of the forward order laws ...
Zhiping Xiong, Zhongshan Liu
doaj +1 more source