相关论文: Matrix Factorizations via the Inverse Function The…

The success of matrix factorizations such as the singular value decomposition (SVD) has motivated the search for even more factorizations. We catalog 53 matrix factorizations, most of which we believe to be new. Our systematic approach,…

In this note we prove that the factorization theorem for dominated polynomials previously proved by the authors is equivalent to an alternative factorization scheme that uses classical linear techniques and a linearization process. However,…

We study the number of factorizations of a positive integer, where the parts of the factorization are of l different colors (or kinds). Recursive or explicit formulas are derived for the case of unordered and ordered, distinct and…

We establish correspondances between factorisations of finite abelian groups (direct factors, unitary factors, non isomorphic subgroup classes) and factorisations of integer matrices. We then study counting functions associated to these…

A spectral factorization theorem is proved for polynomial rank-deficient matrix-functions. The theorem is used to construct paraunitary matrix-functions with first rows given.

This paper presents a sequential randomized lowrank matrix factorization approach for incrementally predicting values of an unknown function at test points using the Gaussian Processes framework. It is well-known that in the Gaussian…

This letter proposes the inverse LDM' and LU factorizations of a matrix partitioned into 2x2 blocks, which include the square-root and division free version. The proposed squareroot and division free inverse LDM' factorization is applied to…

This paper highlights a formal connection between two families of widely used matrix factorization algorithms in numerical linear algebra. One family consists of the Jacobi eigenvalue algorithm and its variants for computing the Hermitian…

Factorization properties of one-loop gauge theory amplitudes have been used as checks on explicitly computed amplitudes and in the construction of ansatze for higher-point ones. In massless theories, such as QCD at high energies, infrared…

We present a simple proof of the factorization of (complex) symmetric matrices into a product of a square matrix and its transpose, and discuss its application in establishing a uniqueness property of certain antilinear operators.

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…

Nonnegative matrix factorization can be used to automatically detect topics within a corpus in an unsupervised fashion. The technique amounts to an approximation of a nonnegative matrix as the product of two nonnegative matrices of lower…

Root subgroup factorization is a refinement of triangular (or LDU) factorization. For a complex reductive Lie group, and a choice of reduced factorization of the longest Weyl group element, the forward map from root subgroup coordinates to…

Matrix factorization is an important mathematical problem encountered in the context of dictionary learning, recommendation systems and machine learning. We introduce a new `decimation' scheme that maps it to neural network models of…

In light of recent data science trends, new interest has fallen in alternative matrix factorizations. By this, we mean various ways of factorizing particular data matrices so that the factors have special properties and reveal insights into…

We show that existing proofs of factorization imply the cancellation of certain multiladder contributions that Gotsman, Levin, and Maor had suggested would invalidate the basic factorization theorem in QCD. No modifications of the original…

We study factorizations of rational matrix functions with simple poles on the Riemann sphere. For the quadratic case (two poles) we show, using multiplicative representations of such matrix functions, that a good coordinate system on this…

In this paper, we study the trade-offs of different inference approaches for Bayesian matrix factorisation methods, which are commonly used for predicting missing values, and for finding patterns in the data. In particular, we consider…

We present a fast variational Bayesian algorithm for performing non-negative matrix factorisation and tri-factorisation. We show that our approach achieves faster convergence per iteration and timestep (wall-clock) than Gibbs sampling and…

We provide an operator space version of Maurey's factorization theorem. The main tool is an embedding result of independent interest. Applications for operator spaces and noncommutative Lp spaces are included.