Related papers: Solving The Ordinary Least Squares in Closed Form,…
Squared tensor networks (TNs) and their generalization as parameterized computational graphs -- squared circuits -- have been recently used as expressive distribution estimators in high dimensions. However, the squaring operation introduces…
Iterative least-squares MR reconstructions typically use the Conjugate Gradient algorithm, despite known numerical issues. This paper demonstrates that the more recent LSMR algorithm has favourable numerical properties, and is to be…
In this work, a new algorithm for solving symmetric indefinite systems of linear equations is presented. It factorizes the matrix into the form LDLt using Jacobi rotations in order to increase the pivot's absolute value. Furthermore, Rook's…
Many applications of generalised linear models (GLMs) can be improved by applying constraints that impose assumptions on the associations or improve consistency of the estimators. Yet, there are still barriers to the implementation and…
We consider the solution of full column-rank least squares problems by means of normal equations that are preconditioned, symmetrically or non-symmetrically, with a randomized preconditioner. With an effective preconditioner, the solutions…
Squared tensor networks (TNs) and their extension as computational graphs--squared circuits--have been used as expressive distribution estimators, yet supporting closed-form marginalization. However, the squaring operation introduces…
We propose a linear algorithm for determining two function parameters by their linear combination. These functions must satisfy the first order differential equations with polynomial coefficients and our parameters are the coefficients of…
Matrix factorization is a popular approach to solving matrix estimation problems based on partial observations. Existing matrix factorization is based on least squares and aims to yield a low-rank matrix to interpret the conditional sample…
We present new algorithms to detect and correct errors in the lower-upper factorization of a matrix, or the triangular linear system solution, over an arbitrary field. Our main algorithms do not require any additional information or…
We conduct a study and comparison of superiorization and optimization approaches for the reconstruction problem of superiorized/regularized least-squares solutions of underdetermined linear equations with nonnegativity variable bounds.…
A new reorthogonalized block classical Gram--Schmidt algorithm is proposed that factorizes a full column rank matrix $A$ into $A=QR$ where $Q$ is left orthogonal (has orthonormal columns) and $R$ is upper triangular and nonsingular. With…
It was recently observed that chiral two-body interactions can be efficiently represented using matrix factorization techniques such as the singular value decomposition. However, the exploitation of these low-rank structures in a few- or…
Sparse linear regression, which entails finding a sparse solution to an underdetermined system of linear equations, can formally be expressed as an $l_0$-constrained least-squares problem. The Orthogonal Least-Squares (OLS) algorithm…
We are presenting a method of linear regression based on Gram-Schmidt orthogonal projection that does not compute a pseudo-inverse matrix. This is useful when we want to make several regressions with random data vectors for simulation…
In this paper we propose a variant of the linear least squares model allowing practitioners to partition the input features into groups of variables that they require to contribute similarly to the final result. The output allows…
The method of ``Total Least Squares'' is proposed as a more natural way (than ordinary least squares) to approximate the data if both the matrix and and the right-hand side are contaminated by ``errors''. In this tutorial note, we give a…
In this paper we propose a quantum algorithm to determine the Tikhonov regularization parameter and solve the ill-conditioned linear equations, for example, arising from the finite element discretization of linear or nonlinear inverse…
A randomized Gram-Schmidt algorithm is developed for orthonormalization of high-dimensional vectors or QR factorization. The proposed process can be less computationally expensive than the classical Gram-Schmidt process while being at least…
Randomized iterative algorithms have recently been proposed to solve large-scale linear systems. In this paper, we present a simple randomized extended block Kaczmarz algorithm that exponentially converges in the mean square to the unique…
In this paper, we leverage over-parameterization to design regularization-free algorithms for the high-dimensional single index model and provide theoretical guarantees for the induced implicit regularization phenomenon. Specifically, we…