Related papers: Tsnnls: A solver for large sparse least squares pr…
The works presented in this habilitation concern the algorithmics of polynomials. This is a central topic in computer algebra, with numerous applications both within and outside the field - cryptography, error-correcting codes, etc. For…
This study shows how to obtain least-squares solutions to initial and boundary value problems to nonhomogeneous linear differential equations with nonconstant coefficients of any order. However, without loss of generality, the approach has…
This work proposes a new moment-SOS hierarchy, called CS-TSSOS, for solving large-scale sparse polynomial optimization problems. Its novelty is to exploit simultaneously correlative sparsity and term sparsity by combining advantages of two…
In numerical linear algebra, considerable effort has been devoted to obtaining faster algorithms for linear systems whose underlying matrices exhibit structural properties. A prominent success story is the method of generalized nested…
As the scale of problems and data used for experimental design, signal processing and data assimilation grow, the oft-occuring least squares subproblems are correspondingly growing in size. As the scale of these least squares problems…
Nonconvex penalty methods for sparse modeling in linear regression have been a topic of fervent interest in recent years. Herein, we study a family of nonconvex penalty functions that we call the trimmed Lasso and that offers exact control…
Network pruning can reduce the high computation cost of deep neural network (DNN) models. However, to maintain their accuracies, sparse models often carry randomly-distributed weights, leading to irregular computations. Consequently, sparse…
Dantzig's vertex pivot simplex method has been published for more than seven decades. Amazingly, it remains one of the most efficient methods to solve linear programming (LP) problem after numerous efforts trying to find some better…
In this paper we present an efficient active-set method for the solution of convex quadratic programming problems with general piecewise-linear terms in the objective, with applications to sparse approximations and risk-minimization. The…
We provide another framework of iterative algorithms based on thresholding, feedback and null space tuning for sparse signal recovery arising in sparse representations and compressed sensing. Several thresholding algorithms with various…
In this paper, a fast algorithm for overcomplete sparse decomposition, called SL0, is proposed. The algorithm is essentially a method for obtaining sparse solutions of underdetermined systems of linear equations, and its applications…
In sparse convolution-type problems, a common technique is to hash the input integers modulo a random prime $p\in [Q/2,Q]$ for some parameter $Q$, which reduces the range of the input integers while preserving their additive structure.…
This work presents a new variation of the commonly used Least Mean Squares Algorithm (LMS) for the identification of sparse signals with an a-priori known sparsity using a hard threshold operator in every iteration. It examines some useful…
We consider the problem of reconstructing an infinite set of sparse, finite-dimensional vectors, that share a common sparsity pattern, from incomplete measurements. This is in contrast to the work [17], where the single vector signal can be…
Significant attention has been given to minimizing a penalized least squares criterion for estimating sparse solutions to large linear systems of equations. The penalty is responsible for inducing sparsity and the natural choice is the…
We present the Residual Quadratic Programming Active-Set Subspace (ResQPASS) method that solves large-scale linear least-squares problems with bound constraints on the variables. The problem is solved by creating a series of small problems…
Inversion of sparse matrices with standard direct solve schemes is robust, but computationally expensive. Iterative solvers, on the other hand, demonstrate better scalability; but, need to be used with an appropriate preconditioner (e.g.,…
In this paper, we revisit the class of iterative shrinkage-thresholding algorithms (ISTA) for solving the linear inverse problem with sparse representation, which arises in signal and image processing. It is shown in the numerical…
We revisit the widely used bss eval metrics for source separation with an eye out for performance. We propose a fast algorithm fixing shortcomings of publicly available implementations. First, we show that the metrics are fully specified by…
Many imaging science tasks can be modeled as a discrete linear inverse problem. Solving linear inverse problems is often challenging, with ill-conditioned operators and potentially non-unique solutions. Embedding prior knowledge, such as…