Related papers: Evaluation of the matrix exponential function usin…
In this paper we propose a method for proving some exponential inequalities based on power series expansion and analysis of derivations of the corresponding functions. Our approach provides a simple proof and generates a new class of…
Exponential time differencing methods is a power tool for high-performance numerical simulation of computationally challenging problems in condensed matter physics, fluid dynamics, chemical and biological physics, where mathematical models…
We construct a finite element method (FEM) for the infinity Laplacian. Solutions of this problem may be singular, which has prompted us to conduct an a posteriori analysis of the method deriving residual based estimators to drive an…
A general framework based on Gaussian models and a MAP-EM algorithm is introduced in this paper for solving matrix/table completion problems. The numerical experiments with the standard and challenging movie ratings data show that the…
Matrix evolution equations occur in many applications, such as dynamical Lyapunov/Sylvester systems or Riccati equations in optimization and stochastic control, machine learning or data assimilation. In many such problems, the dominant…
We develop an empirical Bayes (EB) algorithm for the matrix completion problems. The EB algorithm is motivated from the singular value shrinkage estimator for matrix means by Efron and Morris (1972). Since the EB algorithm is essentially…
Estimating the diagonal entries of a matrix, that is not directly accessible but only available as a linear operator in the form of a computer routine, is a common necessity in many computational applications, especially in image…
We develop a class of integrals on a manifold M called exponential iterated integrals, an extension of K. T. Chen's iterated integrals. It is shown that the matrix entries of any upper triangular representation of the fundamental group of M…
We develop an algorithm for computing the solution of a large system of linear ordinary differential equations (ODEs) with polynomial inhomogeneity. This is equivalent to computing the action of a certain matrix function on the vector…
This paper addresses differential inference in time-varying parametric probabilistic models, like graphical models with changing structures. Instead of estimating a high-dimensional model at each time point and estimating changes later, we…
We develop moment estimators for the parameters of affine stochastic volatility models. We first address the challenge of calculating moments for the models by introducing a recursive equation for deriving closed-form expressions for…
We develop several efficient algorithms for the classical \emph{Matrix Scaling} problem, which is used in many diverse areas, from preconditioning linear systems to approximation of the permanent. On an input $n\times n$ matrix $A$, this…
In this work, we explore a time-fractional diffusion equation of order $\alpha \in (0,1)$ with a stochastic diffusivity parameter. We focus on efficient estimation of the expected values (considered as an infinite dimensional integral on…
The theory of formal power series and derivation is developed from the point of view of the power matrix. A Loewner equation for formal power series is introduced. We then show that the matrix exponential is surjective onto the group of…
Probabilistic argumentation allows reasoning about argumentation problems in a way that is well-founded by probability theory. However, in practice, this approach can be severely limited by the fact that probabilities are defined by adding…
The effort to generate matrix exponentials and associated differentials, required to determine the time evolution of quantum systems, frequently constrains the evaluation of problems in quantum control theory, variational circuit…
We propose an inference procedure for estimators defined by mathematical programming problems, focusing on the important special cases of linear programming (LP) and quadratic programming (QP). In these settings, the coefficients in both…
The initial value problem is introduced after a thorough review of the essential geometry. The initial value equations are put into elliptic form using both conformal transformations and a treatment of the extrinsic curvature introduced…
In this paper, we study the truncated matrix moment problem in one variable through recursive matrix extensions. \ We give necessary and sufficient conditions for a recursive matrix extension of finite data to be a matrix moment sequence in…
Consider a rectangular matrix describing some type of communication or transportation between a set of origins and a set of destinations, or a classification of objects by two attributes. The problem is to infer the entries of the matrix…