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Can one recover a matrix efficiently from only matrix-vector products? If so, how many are needed? This paper describes algorithms to recover matrices with known structures, such as tridiagonal, Toeplitz, Toeplitz-like, and hierarchical…
A cumbersome operation in many scientific fields, is inverting large full-rank matrices. In this paper, we propose a coded computing approach for recovering matrix inverse approximations. We first present an approximate matrix inversion…
We consider a problem of considerable practical interest: the recovery of a data matrix from a sampling of its entries. Suppose that we observe m entries selected uniformly at random from a matrix M. Can we complete the matrix and recover…
We present an algorithm to reduce the computational effort for the multiplication of a given matrix with an unknown column vector. The algorithm decomposes the given matrix into a product of matrices whose entries are either zero or integer…
We consider the problem of accurately recovering a matrix B of size M by M , which represents a probability distribution over M2 outcomes, given access to an observed matrix of "counts" generated by taking independent samples from the…
In this paper a novel approach for matrix manipulation and indexing is proposed .Here the elements in a row of matrix are designated by numeric value called permutation index followed by the elements of the row being randomised. This is…
In matrix recovery from random linear measurements, one is interested in recovering an unknown $M$-by-$N$ matrix $X_0$ from $n<MN$ measurements $y_i=Tr(A_i^T X_0)$ where each $A_i$ is an $M$-by-$N$ measurement matrix with i.i.d random…
A new scaling and recovering algorithm is proposed for simultaneously computing the matrix $\varphi$-functions that arise in exponential integrator methods for the numerical solution of certain first-order systems of ordinary differential…
We consider the problem of estimation of a low-rank matrix from a limited number of noisy rank-one projections. In particular, we propose two fast, non-convex \emph{proper} algorithms for matrix recovery and support them with rigorous…
Given some binary matrix $M$, suppose we are presented with the collection of its rows and columns in independent arbitrary orderings. From this information, are we able to recover the unique original orderings and matrix? We present an…
In this work, we consider the problem of secure multi-party computation (MPC), consisting of $\Gamma$ sources, each has access to a large private matrix, $N$ processing nodes or workers, and one data collector or master. The master is…
We study a matrix recovery problem with unknown correspondence: given the observation matrix $M_o=[A,\tilde P B]$, where $\tilde P$ is an unknown permutation matrix, we aim to recover the underlying matrix $M=[A,B]$. Such problem commonly…
This paper develops new methods to recover the missing entries of a high-rank or even full-rank matrix when the intrinsic dimension of the data is low compared to the ambient dimension. Specifically, we assume that the columns of a matrix…
This paper aims to recover a multi-subspace matrix from permuted data: given a matrix, in which the columns are drawn from a union of low-dimensional subspaces and some columns are corrupted by permutations on their entries, recover the…
In this paper, we study the problem of matrix recovery, which aims to restore a target matrix of authentic samples from grossly corrupted observations. Most of the existing methods, such as the well-known Robust Principal Component Analysis…
In this paper, we consider matrix completion from non-uniformly sampled entries including fully observed and partially observed columns. Specifically, we assume that a small number of columns are randomly selected and fully observed, and…
We introduce a two step algorithm with theoretical guarantees to recover a jointly sparse and low-rank matrix from undersampled measurements of its columns. The algorithm first estimates the row subspace of the matrix using a set of common…
The inversion of extremely high order matrices has been a challenging task because of the limited processing and memory capacity of conventional computers. In a scenario in which the data does not fit in memory, it is worth to consider…
In this paper we show how to recover a spectral approximations to broad classes of structured matrices using only a polylogarithmic number of adaptive linear measurements to either the matrix or its inverse. Leveraging this result we obtain…
The aim of the paper is to provide a constructive method for recovering a unitary matrix from experimental data. Since there is a natural immersion of unitary matrices within the set of double stochastic ones, the problem to solve is to…