Related papers: Meromorphic solutions of recurrence relations and …
The goal of this paper is to present an algebraic approach to the basic results of the theory of linear recurrence relations. This approach is based on the ideas from the theory of representations of one endomorphisms (a special case of…
Let D be a bounded domain in the complex plane whose boundary bD consists of finitely many pairwise disjoint real analytic simple closed curves. Let f be an integrable function on bD. In the paper we show how to compute the candidates for…
General computational methods based on descriptor state-space realizations are proposed to compute coprime factorizations of rational matrices with minimum degree denominators. The new methods rely on recursive pole dislocation techniques,…
The Douglas-Rachford (DR) algorithm is an iterative procedure that uses sequential reflections onto convex sets and which has become popular for convex feasibility problems. In this paper we propose a structural generalization that allows…
For an autonomous system of ordinary differential equations, the existence of a meromorphic general solution is equivalent to the Painlev\'e property, which is widely used to detect integrability. We find all meromorphic solutions of a…
Multiple orthogonal polynomials satisfy a number of recurrence relations, in particular there is a $(r+2)$-term recurrence relation connecting the type II multiple orthogonal polynomials near the diagonal (the so-called step-line recurrence…
From molecular imaging to wireless communications, the ability to align and reconstruct signals from multiple misaligned observations is crucial for system performance. We study the problem of multi-reference alignment (MRA), which arises…
A recurrence equation is a discrete integrable equation whose solutions are all periodic and the period is fixed. We show that infinitely many recurrence equations can be derived from the information about invariant varieties of periodic…
Multiscale methods for second order elliptic equations based on non-overlapping domain decomposition schemes have great potential to take advantage of multi-core, state-of-the-art parallel computers. These methods typically involve solving…
This paper is part of a program that aims to understand the connection between the emergence of chaotic behaviour in dynamical systems in relation with the multi-valuedness of the solutions as functions of complex time $\tau$. In this work…
We derive the recurrence relations for relativistic Coulomb integrals directly from the integral representations with the help of computer algebra methods. In order to manage the computational complexity of this problem, we employ holonomic…
We derive recurrence relations between phase space expressions in different dimensions by confining some of the coordinates to tori or spheres of radius $R$ and taking the limit as $R \to \infty$. These relations take the form of mass…
We present a method to obtain analytic results in terms of multiple polylogarithms for one-loop triangle, box and pentagon integrals depending on an arbitrary number of scales and to any desired order in the Laurent expansion in the…
A set of recurrence relations for on-shell two-loop self-energy diagrams with one mass is presented, which allows to reduce the diagrams with arbitrary indices (powers of scalar propagators) to a set of the master integrals. The SHELL2…
Generalized strata of meromorphic differentials are loci in the usual strata of differentials, where certain sets of residues sum up to zero. They appear naturally in the boundary of the multi-scale compactification of the usual strata.…
We present a method able to recover location and residue of poles of functions meromorphic in a half--plane from samples of the function on the real positive semi-axis. The function is assumed to satisfy appropriate asymptotic conditions…
Using integration by parts relations, Feynman integrals can be represented in terms of coupled systems of differential equations. In the following we suppose that the unknown Feynman integrals can be given in power series representations,…
Recurrence quantification analysis (RQA) is a widely used tool for studying complex dynamical systems, but its standard implementation requires computationally expensive calculations of recurrence plots (RPs) and line length histograms.…
A set of recursive relations satisfied by Selberg-type integrals involving monomial symmetric polynomials are derived, generalizing previously known results. These formulas provide a well-defined algorithm for computing Selberg-Schur…
We develop a new approach to recurrence and the existence of non-constant harmonic functions on infinite weighted graphs. The approach is based on the capacity of subsets of metric boundaries with respect to intrinsic metrics. The main tool…