Related papers: Faster Sparse Matrix Inversion and Rank Computatio…

Since being analyzed by Rokhlin, Szlam, and Tygert and popularized by Halko, Martinsson, and Tropp, randomized Simultaneous Power Iteration has become the method of choice for approximate singular value decomposition. It is more accurate…

We present algorithms to compute the Smith Normal Form of matrices over two families of local rings. The algorithms use the \emph{black-box} model which is suitable for sparse and structured matrices. The algorithms depend on a number of…

Fast matrix multiplication can be described as searching for low-rank decompositions of the matrix--multiplication tensor. We design a neural architecture, \textsc{StrassenNet}, which reproduces the Strassen algorithm for $2\times 2$…

Recovery of low-rank matrices has recently seen significant activity in many areas of science and engineering, motivated by recent theoretical results for exact reconstruction guarantees and interesting practical applications. A number of…

We provide a computational framework for approximating a class of structured matrices; here, the term structure is very general, and may refer to a regular sparsity pattern (e.g., block-banded), or be more highly structured (e.g., symmetric…

Solving symmetric positive definite linear problems is a fundamental computational task in machine learning. The exact solution, famously, is cubicly expensive in the size of the matrix. To alleviate this problem, several linear-time…

This paper studies the problem of reconstructing spectrally sparse signals from a small random subset of time domain samples via low-rank Hankel matrix completion with the aid of prior information. By leveraging the low-rank structure of…

Standard regularization methods that are used to compute solutions to ill-posed inverse problems require knowledge of the forward model. In many real-life applications, the forward model is not known, but training data is readily available.…

Recently, mapping a signal/image into a low rank Hankel/Toeplitz matrix has become an emerging alternative to the traditional sparse regularization, due to its ability to alleviate the basis mismatch between the true support in the…

This article presents a fast solver for the dense "frontal" matrices that arise from the multifrontal sparse elimination process of 3D elliptic PDEs. The solver relies on the fact that these matrices can be efficiently represented as a…

Square matrices appear in many machine learning problems and models. Optimization over a large square matrix is expensive in memory and in time. Therefore an economic approximation is needed. Conventional approximation approaches factorize…

This paper studies the robust Hankel recovery problem, which simultaneously removes the sparse outliers and fulfills missing entries from the partial observation. We propose a novel non-convex algorithm, coined Hankel Structured Newton-Like…

While quantum algorithms for solving large scale systems of linear equations offer potentially exponential speedups, their application has largely been confined to sparse matrices. This work extends the scope of these algorithms to a broad…

The computational complexity of different steps of the basic SSA is discussed. It is shown that the use of the general-purpose "blackbox" routines (e.g. found in packages like LAPACK) leads to huge waste of time resources since the special…

This paper proposes a new method for estimating sparse precision matrices in the high dimensional setting. It has been popular to study fast computation and adaptive procedures for this problem. We propose a novel approach, called Sparse…

Matrix-vector multiplication is one of the most fundamental computing primitives. Given a matrix $A\in\mathbb{F}^{N\times N}$ and a vector $b$, it is known that in the worst case $\Theta(N^2)$ operations over $\mathbb{F}$ are needed to…

We consider the problem of recovering an $n_1 \times n_2$ low-rank matrix with $k$-sparse singular vectors from a small number of linear measurements (sketch). We propose a sketching scheme and an algorithm that can recover the singular…

In this paper we consider the low-rank matrix completion problem with specific application to forecasting in time series analysis. Briefly, the low-rank matrix completion problem is the problem of imputing missing values of a matrix under a…

Low-rank matrix regression is a fundamental problem in data science with various applications in systems and control. Nuclear norm regularization has been widely applied to solve this problem due to its convexity. However, it suffers from…

Existing block Kaczmarz methods face challenges in balancing computational efficiency and convergence for large sparse linear systems with scattered nonzero patterns, due to costly partitioning strategies and non-orthogonal projections. In…