Related papers: The double splitting iteration method for solving …
iALS is a popular algorithm for learning matrix factorization models from implicit feedback with alternating least squares. This algorithm was invented over a decade ago but still shows competitive quality compared to recent approaches like…
Recently Ahmadi et al. (2021) and Tagliaferro (2022) proposed some iterative methods for the numerical solution of linear systems which, under the classical hypothesis of strict diagonal dominance, typically converge faster than the Jacobi…
We present a new, simple and computationally efficient iterative method for low rank matrix completion. Our method is inspired by the class of factorization-type iterative algorithms, but substantially differs from them in the way the…
A new iterative technique is presented for solving of initial value problem for certain classes of multidimensional linear and nonlinear partial differential equations. Proposed iterative scheme does not require any discretization,…
An iteratively reweighted least squares (IRLS) method is proposed for estimating polyserial and polychoric correlation coefficients in this paper. It iteratively calculates the slopes in a series of weighted linear regression models fitting…
The classical iteratively reweighted least-squares (IRLS) algorithm aims to recover an unknown signal from linear measurements by performing a sequence of weighted least squares problems, where the weights are recursively updated at each…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
We consider the computation of the matrix logarithm by using numerical quadrature. The efficiency of numerical quadrature depends on the integrand and the choice of quadrature formula. The Gauss--Legendre quadrature has been conventionally…
This work presents a general framework for solving the low rank and/or sparse matrix minimization problems, which may involve multiple non-smooth terms. The Iteratively Reweighted Least Squares (IRLS) method is a fast solver, which smooths…
We present a method for solving the general mixed constrained convex quadratic programming problem using an active set method on the dual problem. The approach is similar to existing active set methods, but we present a new way of solving…
We propose a variational splitting technique for the generalized-$\alpha$ method to solve hyperbolic partial differential equations. We use tensor-product meshes to develop the splitting method, which has a computational cost that grows…
LSMR is a widely recognized method for solving least squares problems via the double QR decomposition. Various preconditioning techniques have been explored to improve its efficiency. One issue that arises when implementing these…
We consider linear inverse problems where the solution is assumed to have a sparse expansion on an arbitrary pre-assigned orthonormal basis. We prove that replacing the usual quadratic regularizing penalties by weighted l^p-penalties on the…
In this paper, we study the problem of finding the least square solutions of over-determined linear algebraic equations over networks in a distributed manner. Each node has access to one of the linear equations and holds a dynamic state. We…
We develop a new least squares method for solving the second-order elliptic equations in non-divergence form. Two least-squares-type functionals are proposed for solving the equations in two steps. We first obtain a numerical approximation…
For a linear complementarity problem, we present a relaxaiton accelerated two-sweep matrix splitting iteration method. The convergence analysis illustrates that the proposed method converges to the exact solution of the linear…
We introduce fast algorithms for solving $\ell_{p}$ regression problems using the iteratively reweighted least squares (IRLS) method. Our approach achieves state-of-the-art iteration complexity, outperforming the IRLS algorithm by…
This paper presents an iteration method for solving linear particle transport problems in binary stochastic mixtures. It is based on nonlinear projection approach. The method is defined by a hierarchy of equations consisting of the…
For solving a wide class of nonconvex and nonsmooth problems, we propose a proximal linearized iteratively reweighted least squares (PL-IRLS) algorithm. We first approximate the original problem by smoothing methods, and second write the…
The work is devoted to the development of numerical methods for computing "formal solutions" of interval systems of linear algebraic equations. These solutions are found in Kaucher interval arithmetic, which extends and completes the…