Related papers: On the final limit of a transition matrix

In this paper we study the problem of computing max-entropy distributions over a discrete set of objects subject to observed marginals. Interest in such distributions arises due to their applicability in areas such as statistical physics,…

We prove a limit theorem on the convergence of the distributions of the scaled last exit time over a slowly moving nonlinear boundary for a class of Gaussian stationary processes. The limit is a double exponential (Gumbel) distribution.

We consider a linear symmetric and elliptic PDE and a linear goal functional. We design and analyze a goal-oriented adaptive finite element method, which steers the adaptive mesh-refinement as well as the approximate solution of the arising…

In this paper, we propose a numerical method for computing Hadamard finite-part integrals with an integral-power singularity at an endpoint, the part of the divergent integral which is finite as a limiting procedure. In the proposed method,…

We describe a dynamic programming algorithm for exact counting and exact uniform sampling of matrices with specified row and column sums. The algorithm runs in polynomial time when the column sums are bounded. Binary or non-negative integer…

Motivated by recent interests in predictive inference under distribution shift, we study the problem of approximating finite weighted exchangeable sequences by a mixture of finite sequences with independent terms. Various bounds are derived…

We propose a recursive algorithm for the numerical computation of the optimal value function $\inf_{t\le\tau\le T} E \Big[\sup_{0\le s\le T } Y_s / Y_{\tau} \big| {\cal F}_t\Big]$ over the stopping times $\tau$ with respect to the…

Computable and sharp error bounds are derived for asymptotic expansions for linear differential equations having a simple turning point. The expansions involve Airy functions and slowly varying coefficient functions. The sharpness of the…

Large statically indeterminate truss and frame structures exhibit complex load-bearing behavior, and redundancy matrices are helpful for their analysis and design. Depending on the task, the full redundancy matrix or only its diagonal…

This is the first of a series of papers in which we study deep computations (ultracomputations) and deep iterates, formalizing the ideas of "asymptotic limit" of computations and compositional iterates, respectively. In this first paper of…

The problem of iterated partial summations is solved for some discrete distributions defined on discrete supports. The power method, usually used as a computational approach to finding matrix eigenvalues and eigenvectors, is in some cases…

In earlier work, we developed an approach for automatic complexity analysis of integer programs, based on an alternating modular inference of upper runtime and size bounds for program parts. In this paper, we show how recent techniques to…

In this paper a new fast algorithm for the computation of the distance of a matrix to a nearby defective matrix is presented. The problem is formulated following Alam & Bora (Linear Algebra Appl., 396 (2005), pp.~273--301) and reduces to…

We introduce a new algorithm to compute the zeta function of a curve over a finite field. This method extends previous work of ours to all curves for which a good lift to characteristic zero is known. We develop all the necessary bounds,…

Peak estimation bounds extreme values of a function of state along trajectories of a dynamical system. This paper focuses on extending peak estimation to continuous and discrete settings with time-independent and time-dependent uncertainty.…

We present efficient approximation of the error function obtained by Fourier expansion of the exponential function $\exp [{- {(t - 2 \sigma)^2}/4}]$. The error analysis reveals that it is highly accurate and can generate numbers that match…

In this paper, we study adaptive finite element approximations in a perturbation framework, which makes use of the existing adaptive finite element analysis of a linear symmetric elliptic problem. We prove the convergence and complexity of…

We construct a finite element approximation of a strain-limiting elastic model on a bounded open domain in $\mathbb{R}^d$, $d \in \{2,3\}$. The sequence of finite element approximations is shown to exhibit strong convergence to the unique…

In our recent publication [1] we presented an exponential series approximation suitable for highly accurate computation of the complex error function in a rapid algorithm. In this Short Communication we describe how a simplified…

We derive a new bound for some bilinear sums over points of an elliptic curve over a finite field. We use this bound to improve a series of previous results on various exponential sums and some arithmetic problems involving points on…