Related papers: On greedy multi-step inertial randomized Kaczmarz …
We present a novel greedy Gauss-Seidel method for solving large linear least squares problem. This method improves the greedy randomized coordinate descent (GRCD) method proposed recently by Bai and Wu [Bai ZZ, and Wu WT. On greedy…
Stochastic iterative algorithms such as the Kaczmarz and Gauss-Seidel methods have gained recent attention because of their speed, simplicity, and the ability to approximately solve large-scale linear systems of equations without needing to…
We study a version of the randomized Kaczmarz algorithm for solving systems of linear equations where the iterates are confined to the solution space of a selected subsystem. We show that the subspace constraint leads to an accelerated…
Randomized iterative algorithms have attracted much attention in recent years because they can approximately solve large-scale linear systems of equations without accessing the entire coefficient matrix. In this paper, we propose two novel…
Sparsity learning with known grouping structure has received considerable attention due to wide modern applications in high-dimensional data analysis. Although advantages of using group information have been well-studied by shrinkage-based…
The Kaczmarz algorithm is a popular solver for overdetermined linear systems due to its simplicity and speed. In this paper, we propose a modification that speeds up the convergence of the randomized Kaczmarz algorithm for systems of linear…
We analyze task orderings in continual learning for linear regression, assuming joint realizability of training data. We focus on orderings that greedily maximize dissimilarity between consecutive tasks, a concept briefly explored in prior…
We present an algorithm to generate application-specific, global reduced order quadratures (ROQ) for multiple fast evaluations of weighted inner products between parameterized functions. If a reduced basis (RB) or any other projection-based…
The method of alternation projections (MAP) is an iterative procedure for finding the projection of a point on the intersection of closed subspaces of an Hilbert space. The convergence of this method is usually slow, and several methods for…
Many complex applications require the solution of initial-value problems where some components change fast, while others vary slowly. Multirate schemes apply different step sizes to resolve different components of the system, according to…
Stochastic iterative methods are useful in a variety of large-scale numerical linear algebraic, machine learning, and statistical problems, in part due to their low-memory footprint. They are frequently used in a variety of applications,…
The Sampling Kaczmarz Motzkin (SKM) algorithm is a generalized method for solving large scale linear systems of inequalities. Having its root in the relaxation method of Agmon, Schoenberg, and Motzkin and the randomized Kaczmarz method, SKM…
Kernel-based schemes are state-of-the-art techniques for learning by data. In this work we extend some ideas about kernel-based greedy algorithms to exponential-polynomial splines, whose main drawback consists in possible overfitting and…
We study Kaczmarz type methods to solve consistent linear matrix equations. We first present a block Kaczmarz (BK) method that employs a deterministic cyclic row selection strategy. Assuming that the associated coefficient matrix has full…
This paper proposes a greedy heuristic named as Big step greedy heuristic and investigates the application of Big step greedy heuristic for maximum k-coverage problem. Greedy algorithms construct the solution in multiple steps, the…
In this work, we propose a cross-layer design strategy based on the parallel interference cancellation (PIC) detection technique and a multi-relay selection algorithm for the uplink of cooperative direct-sequence code-division multiple…
The Kaczmarz method for solving linear systems of equations is an iterative algorithm that has found many applications ranging from computer tomography to digital signal processing. Despite the popularity of this method, useful theoretical…
Accurate online inertial parameter estimation is essential for adaptive robotic control, enabling real-time adjustment to payload changes, environmental interactions, and system wear. Traditional methods often struggle to track abrupt…
In this paper, we propose a randomized accelerated method for the minimization of a strongly convex function under linear constraints. The method is of Kaczmarz-type, i.e. it only uses a single linear equation in each iteration. To obtain…
We provide a complete characterization of the randomized Kaczmarz algorithm (RKA) for inconsistent linear systems. The Kaczmarz algorithm, known in some fields as the algebraic reconstruction technique, is a classical method for solving…