相关论文: Common Factors in Fraction-Free Matrix Decompositi…

We consider exact matrix decomposition by Gauss-Bareiss reduction. We investigate two aspects of the process: common row and column factors and the influence of pivoting strategies. We identify two types of common factors: systematic and…

We consider the factorization of a rectangular matrix $X $ into a positive linear combination of rank-one factors of the form $u v^\top$, where $u$ and $v$ belongs to certain sets $\mathcal{U}$ and $\mathcal{V}$, that may encode specific…

We introduce a Generalized Randomized QR-decomposition that may be applied to arbitrary products of matrices and their inverses, without needing to explicitly compute the products or inverses. This factorization is a critical part of a…

Given an element $f$ in a regular local ring, we study matrix factorizations of $f$ with $d \ge 2$ factors, that is, we study tuples of square matrices $(\varphi_1,\varphi_2,\dots,\varphi_d)$ such that their product is $f$ times an identity…

An observed $K$-dimensional series $\left\{ y_{n}\right\} _{n=1}^{N}$ is expressed in terms of a lower $p$-dimensional latent series called factors $f_{n}$ and random noise $\varepsilon_{n}$. The equation, $y_{n}=Qf_{n}+\varepsilon_{n}$ is…

We consider the problem of estimating high-dimensional covariance matrices of a particular structure, which is a summation of low rank and sparse matrices. This covariance structure has a wide range of applications including factor analysis…

It has been shown that for a certain special type of quantum graphs the random-matrix form factor can be recovered to at least third order in the scaled time \tau using periodic-orbit theory. Two types of contributing pairs of orbits were…

There are two approaches to time series approximate factor models: the static factor model, where the factors are loaded contemporaneously by the common component, and the Generalised Dynamic Factor Model, where the factors are loaded with…

Graphical models represent multivariate and generally not normalized probability distributions. Computing the normalization factor, called the partition function, is the main inference challenge relevant to multiple statistical and…

The matrix LU factorization algorithm is a fundamental algorithm in linear algebra. We propose a generalization of the LU and LEU algorithms to accommodate the case of a commutative domain and its field of quotients. This algorithm…

We investigate a general matrix factorization for deviance-based data losses, extending the ubiquitous singular value decomposition beyond squared error loss. While similar approaches have been explored before, our method leverages…

We propose a novel approach to estimating the precision matrix of multivariate Gaussian data that relies on decomposing them into a low-rank and a diagonal component. Such decompositions are very popular for modeling large covariance…

The decay of a general time dependent structure factors is considered. The dynamics is that of stochastic field equations of the Langevin type, where the systematic generalized force is a functional derivative of some classical field…

We use the periodicity properties of generalized Gauss sums to factor numbers. Moreover, we derive rules for finding the factors and illustrate this factorization scheme for various examples. This algorithm relies solely on interference and…

For certain types of quantum graphs we show that the random-matrix form factor can be recovered to at least third order in the scaled time $\tau$ from periodic-orbit theory. We consider the contributions from pairs of periodic orbits…

Every fraction is a union of points, which are trivial regular fractions. To characterize non trivial decomposition, we derive a condition for the inclusion of a regular fraction as follows. Let $F = \sum_\alpha b_\alpha X^\alpha$ be the…

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…

I propose a way to use non-Euclidean norms to formulate a QR-like factorization which can unlock interesting and potentially useful properties of non-Euclidean norms - for example the ability of $l^1$ norm to suppresss outliers or promote…

Low-rank matrix approximations, such as the truncated singular value decomposition and the rank-revealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which…

Many known models, which generally use a factorization hypothesis, give a poor account of the decays B into J/psi + K(*). Usually there is a free overall factor, which is fit to the data, so that tests of the models rely upon ratios. The…