Related papers: Factorization Method in Curvilinear Coordinates an…
In this survey paper we study parametric versions of writing a matrix in $SL_n (\mathbb{C})$ as a product of lower and upper unitriangular matrices in interchanging order as well as generalizations to other classical groups. We give an…
We introduce meta-factorization, a theory that describes matrix decompositions as solutions of linear matrix equations: the projector and the reconstruction equation. Meta-factorization reconstructs known factorizations, reveals their…
In continuation to our recent work on noncommutative polynomial factorization, we consider the factorization problem for matrices of polynomials and show the following results. (1) Given as input a full rank $d\times d$ matrix $M$ whose…
Matrix factorization is a popular approach for large-scale matrix completion. The optimization formulation based on matrix factorization can be solved very efficiently by standard algorithms in practice. However, due to the non-convexity…
With the recent success of representation learning methods, which includes deep learning as a special case, there has been considerable interest in developing representation learning techniques that can incorporate known physical…
Monte Carlo simulations of systems with a complex action are known to be extremely difficult. A new approach to this problem based on a factorization property of distribution functions of observables has been proposed recently. The method…
High-order methods gain more and more attention in computational fluid dynamics. However, the potential advantage of these methods depends critically on the availability of efficient elliptic solvers. With spectral-element methods, static…
Matrix factorization techniques have been widely used as a method for collaborative filtering for recommender systems. In recent times, different variants of deep learning algorithms have been explored in this setting to improve the task of…
Completely positive factorization (CPF) is a critical task with applications in many fields. This paper proposes a novel method for the CPF. Based on the idea of exterior point iteration, an optimization model is given, which aims to…
We give a number of explicit matrix-algorithms for analysis/synthesis in multi-phase filtering; i.e., the operation on discrete-time signals which allow a separation into frequency-band components, one for each of the ranges of bands, say…
Gradient descent for matrix factorization exhibits an implicit bias toward approximately low-rank solutions. While existing theories often assume the boundedness of iterates, empirically the bias persists even with unbounded sequences. This…
Polarization is a unique characteristic of transverse wave and is represented by Stokes parameters. Analysis of polarization states can reveal valuable information about the sources. In this paper, we propose a separable low-rank quaternion…
Factorization -- a simple form of standardization -- is concerned with reduction strategies, i.e. how a result is computed. We present a new technique for proving factorization theorems for compound rewriting systems in a modular way, which…
The problem of matrix factorization motivated by diffraction or elasticity is studied. A powerful tool for analyzing its solutions is introduced, namely analytical continuation formulae are derived. Necessary condition for commutative…
Nonnegative matrix factorization (NMF) is a popular method used to reduce dimensionality in data sets whose elements are nonnegative. It does so by decomposing the data set of interest, $\mathbf{X}$, into two lower rank nonnegative matrices…
Factor models are widely used across diverse areas of application for purposes that include dimensionality reduction, covariance estimation, and feature engineering. Traditional factor models can be seen as an instance of linear embedding…
Qutrits, the triple level quantum systems in various forms, have been proposed for quantum information processing recently. By the methods presented in this paper a bi-photonic qutrit, which is encoded with the polarizations of two photons…
Matrices with off-diagonal decay appear in a variety of fields in mathematics and in numerous applications, such as signal processing, statistics, communications engineering, condensed matter physics, and quantum chemistry. Numerical…
We show how to use the method of orthogonal polynomials for integrating, in the planar approximation, the partition function of one-matrix models with a potential with even or odd vertices, or any combination of them.
In finance, economics and many other fields, observations in a matrix form are often observed over time. For example, many economic indicators are obtained in different countries over time. Various financial characteristics of many…