Related papers: Krylov iterative methods for linear least squares …
There are many practical applications based on the Least Square Error (LSE) or Total Least Square Error (TLSE) methods. Usually the standard least square error is used due to its simplicity, but it is not an optimal solution, as it does not…
Krylov subspace methods are a powerful family of iterative solvers for linear systems of equations, which are commonly used for inverse problems due to their intrinsic regularization properties. Moreover, these methods are naturally suited…
Simulating diffusion in heterogeneous media presents a significant computational challenge, as resolving microscopic physical scales traditionally demands excessively fine computational grids. To overcome this barrier, we extend the…
In the present paper, we propose Krylov-based methods for solving large-scale differential Sylvester matrix equations having a low rank constant term. We present two new approaches for solving such differential matrix equations. The first…
We study randomized sketching methods for approximately solving least-squares problem with a general convex constraint. The quality of a least-squares approximation can be assessed in different ways: either in terms of the value of the…
Clarksons algorithm is a two-staged randomized algorithm for solving linear programs. This algorithm has been simplified and adapted to fit the framework of LP-type problems. In this framework we can tackle a number of non-linear problems…
Bivariate matrix functions provide a unified framework for various tasks in numerical linear algebra, including the solution of linear matrix equations and the application of the Fr\'echet derivative. In this work, we propose a novel…
LSQR, a Lanczos bidiagonalization based Krylov subspace iterative method, and its mathematically equivalent CGLS applied to normal equations system, are commonly used for large-scale discrete ill-posed problems. It is well known that LSQR…
The alternating least squares algorithm for CP and Tucker decomposition is dominated in cost by the tensor contractions necessary to set up the quadratic optimization subproblems. We introduce a novel family of algorithms that uses…
When a solution to an abstract inverse linear problem on Hilbert space is approximable by finite linear combinations of vectors from the cyclic subspace associated with the datum and with the linear operator of the problem, the solution is…
Based on the joint bidiagonalization process of a large matrix pair $\{A,L\}$, we propose and develop an iterative regularization algorithm for the large scale linear discrete ill-posed problems in general-form regularization: $\min\|Lx\| \…
Model reduction simplifies complex dynamical systems while preserving essential properties. This paper revisits a recently proposed system-theoretic framework for least squares moment matching. It interprets least squares model reduction in…
Iterative solvers for large-scale linear systems such as Krylov subspace methods can diverge when the linear system is ill-conditioned, thus significantly reducing the applicability of these iterative methods in practice 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…
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 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 nonlinear sea-ice problem is considered in a least-squares finite element setting. The corresponding variational formulation approximating simultaneously the stress tensor and the velocity is analysed. In particular, the least-squares…
We present a variational algorithm for solving the classical inverse Sturm-Liouville problem in one dimension when two spectra are given. All critical points of the least squares functional are at global minima, which which suggests…
Consider the generalized linear least squares (GLS) problem $\min\|Lx\|_2 \ \mathrm{s.t.} \ \|M(Ax-b)\|_2=\min$. The weighted pseudoinverse $A_{ML}^{\dag}$ is the matrix that maps $b$ to the minimum 2-norm solution of this GLS problem. By…
Several Krylov-type procedures are introduced that generalize matrix Krylov methods for tensor computations. They are denoted minimal Krylov recursion, maximal Krylov recursion, contracted tensor product Krylov recursion. It is proved that…