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The matrix completion problem has been studied broadly under many underlying conditions. The problem has been explored under adaptive or non-adaptive, exact or estimation, single-phase or multi-phase, and many other categories. In most of…
Many important applications across science, data analytics, and AI workloads depend on distributed matrix multiplication. Prior work has developed a large array of algorithms suitable for different problem sizes and partitionings including…
In this paper we present an efficient iterative method of order six for the inclusion of the inverse of a given regular matrix. To provide the upper error bound of the outer matrix for the inverse matrix, we combine point and interval…
In this paper, we introduce a new way of constructing and decoding multipermutation codes. Multipermutations are permutations of a multiset that generally consist of duplicate entries. We first introduce a class of binary matrices called…
This paper is an attempt to remedy the problem of slow convergence for first-order numerical algorithms by proposing an adaptive conditioning heuristic. First, we propose a parallelizable numerical algorithm that is capable of solving…
The low-rank matrix factorization as a L1 norm minimization problem has recently attracted much attention due to its intrinsic robustness to the presence of outliers and missing data. In this paper, we propose a new method, called the…
The objective of this research was to compute the principal matrix square root with sparse approximation. A new stable iterative scheme avoiding fully matrix inversion (SIAI) is provided. The analysis on the sparsity and error of the…
Error-correcting codes are a method for representing data, so that one can recover the original information even if some parts of it were corrupted. The basic idea, which dates back to the revolutionary work of Shannon and Hamming about a…
Matrix multiplication over the real field constitutes a foundational operation in the training of deep learning models, serving as a computational cornerstone for both forward and backward propagation processes. However, the presence of…
The theory of quantum error correction was established more than a decade ago as the primary tool for fighting decoherence in quantum information processing. Although great progress has already been made in this field, limited methods are…
We construct new symmetric Hadamard matrices of orders $92,116$, and $172$. While the existence of those of order $92$ was known since 1978, the orders $116$ and $172$ are new. Our construction is based on a recent new combinatorial array…
We propose a general framework for reconstructing and denoising single entries of incomplete and noisy entries. We describe: effective algorithms for deciding if and entry can be reconstructed and, if so, for reconstructing and denoising…
As an approximate nearest neighbor search technique, hashing has been widely applied in large-scale image retrieval due to its excellent efficiency. Most supervised deep hashing methods have similar loss designs with embedding learning,…
When a matrix A with n columns is known to be well approximated by a linear combination of basis matrices B_1,..., B_p, we can apply A to a random vector and solve a linear system to recover this linear combination. The same technique can…
We study recovering parity check relations for an unknown code from intercepted bitstream received from Binary Symmetric Channel in this paper. An iterative column elimination algorithm is introduced which attempts to eliminate parity bits…
Encoding data as a set of unordered strings is receiving great attention as it captures one of the basic features of DNA storage systems. However, the challenge of constructing optimal redundancy codes for this channel remained elusive. In…
It is widely known that the lower bound for the algorithmic complexity of square matrix multiplication resorts to at least $n^2$ arithmetic operations. The justification builds upon the following reasoning: given that there are $2 n^2$…
We consider the problem of sparse matrix multiplication by the column row method in a distributed setting where the matrix product is not necessarily sparse. We present a surprisingly simple method for "consistent" parallel processing of…
In this paper, we introduce a powerful technique based on Leave-one-out analysis to the study of low-rank matrix completion problems. Using this technique, we develop a general approach for obtaining fine-grained, entrywise bounds for…
Sparse estimation of the precision matrix under high-dimensional scaling constitutes a canonical problem in statistics and machine learning. Numerous regression and likelihood based approaches, many frequentist and some Bayesian in nature…