Related papers: Fast randomized least-squares solvers can be just …
This paper studies the solution of nonsymmetric linear systems by preconditioned Krylov methods based on the normal equations, LSQR in particular. On some examples, preconditioned LSQR is seen to produce errors many orders of magnitude…
We describe an efficient method for the approximation of functions using radial basis functions (RBFs), and extend this to a solver for boundary value problems on irregular domains. The method is based on RBFs with centers on a regular grid…
Recursive estimates of large systems of equations in the context of least squares fitting is a common practice in different fields of study. For example, recursive adaptive filtering is extensively used in signal processing and control…
We propose a deep learning approach to the obstacle problem inspired by the first-order system least-squares (FOSLS) framework. This method reformulates the problem as a convex minimization task; by simultaneously approximating the…
Linear solvers are major computational bottlenecks in a wide range of decision support and optimization computations. The challenges become even more pronounced on heterogeneous hardware, where traditional sparse numerical linear algebra…
Sketching-based preconditioners have been shown to accelerate the solution of dense least-squares problems with coefficient matrices having substantially more rows than columns. The cost of generating these preconditioners can be reduced by…
We consider to design a new efficient and easy-to-implement algorithm to solve a general group sparse optimization model with a class of non-convex non-Lipschitz regularizations, named as fast iterative thresholding and support-and-scale…
We present a novel iterative algorithm for approximating the linear least squares solution with low complexity. After a motivation of the algorithm we discuss the algorithm's properties including its complexity, and we present theoretical…
Linear systems in applications are typically well-posed, and yet the coefficient matrices may be nearly singular in that the condition number $\kappa(\boldsymbol{A})$ may be close to $1/\varepsilon_{w}$, where $\varepsilon_{w}$ denotes the…
Recursive least squares (RLS) algorithms were once widely used for training small-scale neural networks, due to their fast convergence. However, previous RLS algorithms are unsuitable for training deep neural networks (DNNs), since they…
In this paper, we consider a squared $L_1/L_2$ regularized model for sparse signal recovery from noisy measurements. We first establish the existence of optimal solutions to the model under mild conditions. Next, we propose a proximal…
We provide an exact analysis of a class of randomized algorithms for solving overdetermined least-squares problems. We consider first-order methods, where the gradients are pre-conditioned by an approximation of the Hessian, based on a…
A numerical method is developed to solve linear semi-infinite programming problem (LSIP) in which the iterates produced by the algorithm are feasible for the original problem. This is achieved by constructing a sequence of standard linear…
Solving an integer least squares (ILS) problem usually consists of two stages: reduction and search. This thesis is concerned with the reduction process for the ordinary ILS problem and the ellipsoid-constrained ILS problem. For the…
This work presents a robust, energy-based deep learning framework for solving transmission problems in heterogeneous media, including cases with discontinuous material scenarios. We introduce a weighted First-Order System Least-Squares…
In this article, we propose a novel Stabilized Physics Informed Neural Networks method (SPINNs) for solving wave equations. In general, this method not only demonstrates theoretical convergence but also exhibits higher efficiency compared…
Neural networks are predominantly trained using gradient-based methods, yet in many applications their final predictions remain far from the accuracy attainable within the model's expressive capacity. We introduce Linearized Subspace…
We consider the problem of efficiently solving large-scale linear least squares problems that have one or more linear constraints that must be satisfied exactly. Whilst some classical approaches are theoretically well founded, they can face…
This paper fortifies the recently introduced hierarchical-optimization recursive least squares (HO-RLS) against outliers which contaminate infrequently linear-regression models. Outliers are modeled as nuisance variables and are estimated…
Inverse problems arise in a wide spectrum of applications in fields ranging from engineering to scientific computation. Connected with the rise of interest in inverse problems is the development and analysis of regularization methods, such…