Related papers: An Implicit Representation and Iterative Solution …

There is an increasing body of work exploring the integration of random projection into algorithms for numerical linear algebra. The primary motivation is to reduce the overall computational cost of processing large datasets. A suitably…

Randomized iterative algorithms, such as the randomized Kaczmarz method, have gained considerable popularity due to their efficacy in solving matrix-vector and matrix-matrix regression problems. Our present work leverages the insights…

Random sketching is a dimensionality reduction technique that approximately preserves norms and singular values up to some $O(1)$ distortion factor with high probability. The most popular sketches in literature are the Gaussian sketch and…

This work discusses tensor network embeddings, which are random matrices ($S$) with tensor network structure. These embeddings have been used to perform dimensionality reduction of tensor network structured inputs $x$ and accelerate…

Efficiently solving sparse linear algebraic equations is an important research topic of numerical simulation. Commonly used approaches include direct methods and iterative methods. Compared with the direct methods, the iterative methods…

Stochastic computing (SC) is a promising candidate for fault tolerant computing in digital circuits. We present a novel stochastic computing estimation architecture allowing to solve a large group of estimation problems including least…

Randomized iterative algorithms have recently been proposed to solve large-scale linear systems. In this paper, we present a simple randomized extended block Kaczmarz algorithm that exponentially converges in the mean square to the unique…

Many relevant machine learning and scientific computing tasks involve high-dimensional linear operators accessible only via costly matrix-vector products. In this context, recent advances in sketched methods have enabled the construction of…

The key challenge in designing a sketch representation lies with handling the abstract and iconic nature of sketches. Existing work predominantly utilizes either, (i) a pixelative format that treats sketches as natural images employing…

For solving the large-scale linear system by iteration methods, we utilize the Petrov-Galerkin conditions and relaxed greedy index selection technique and provide two relaxed greedy deterministic row (RGDR) and column (RGDC) iterative…

Count-sketch is a popular matrix sketching algorithm that can produce a sketch of an input data matrix X in O(nnz(X))time where nnz(X) denotes the number of non-zero entries in X. The sketched matrix will be much smaller than X while…

Randomized algorithms are important for solving large-scale optimization problems. In this paper, we propose a fast sketching algorithm for least square problems regularized by convex or nonconvex regularization functions, Sketching for…

We present a randomized iterative algorithm that exponentially converges in expectation to the minimum Euclidean norm least squares solution of a given linear system of equations. The expected number of arithmetic operations required to…

Massive MIMO system yields significant improvements in spectral and energy efficiency for future wireless communication systems. The regularized zero-forcing (RZF) beamforming is able to provide good performance with the capability of…

Linear sketching algorithms have been widely used for processing large-scale distributed and streaming datasets. Their popularity is largely due to the fact that linear sketches can be naturally composed in the distributed model and be…

When solving noisy linear systems Ax = b + c, the theoretical and empirical performance of stochastic iterative methods, such as the Randomized Kaczmarz algorithm, depends on the noise level. However, if there are a small number of highly…

A greedy randomized augmented Kaczmarz (GRAK) method was proposed in [Z.-Z. Bai and W.-T. WU, SIAM J. Sci. Comput., 43 (2021), pp. A3892-A3911] for large and sparse inconsistent linear systems. However, one has to construct two new index…

Linear constrained switching systems are linear switched systems whose switching sequences are constrained by a deterministic finite automaton. This work investigates how to generate a sequence of matrices with an asymptotic growth rate…

The sketch-and-project (SAP) framework for solving systems of linear equations has unified the theory behind popular projective iterative methods such as randomized Kaczmarz, randomized coordinate descent, and variants thereof. The…

Purpose: Parallel imaging and compressed sensing reconstructions of large MRI datasets often have a prohibitive computational cost that bottlenecks clinical deployment, especially for 3D non-Cartesian acquisitions. One common approach is to…