Related papers: A new algorithm for computing the asymptotic solut…
We present a linear time algorithm for computing a cycle separator in a planar graph that is (arguably) simpler than previously known algorithms. Our algorithm builds on, and is somewhat similar to, previous algorithms for computing…
We present an algorithm to solve a system of diagonal polynomial equations over finite fields when the number of variables is greater than some fixed polynomial of the number of equations whose degree depends only on the degree of the…
Dynamical systems with quadratic or polynomial drift exhibit complex dynamics, yet compared to nonlinear systems in general form, are often easier to analyze, simulate, control, and learn. Results going back over a century have shown that…
In this paper we continue our earlier investigations into the asymptotic behaviour of infinite systems of coupled differential equations. Under the mild assumption that the so-called characteristic function of our system is completely…
We consider first-order linear systems of ordinary differential equations with periodic coefficients. Supposing that right-hand sides of equations are not known and subjected to some quadratic restrictions, we obtain optimal, in certain…
The work is devoted to the construction of a new interval arithmetic which would combine algorithmic efficiency and high quality estimation of the ranges of expressions.
The application of the approximation-operational approach to solving linear differential equations of fractional order with variable coefficients is considered. It is shown that the method can also be applied to solving differential…
In this note, we present a new numerical method for solving backward stochastic differential equations. Our method can be viewed as an analogue of the classical finite element method solving deterministic partial differential equations.
Estimating and detecting faults is crucial in ensuring safe and efficient automated systems. In the presence of disturbances, noise or varying system dynamics, such estimation is even more challenging. To address this challenge, this…
The linear complete differential resultant of a finite set of linear ordinary differential polynomials is defined. We study the computation by linear complete differential resultants of the implicit equation of a system of $n$ linear…
We consider how the Pad'e-Borel, Pad'e-Borel-Leroy, and conformal mapping summation methods for asymptotic series can be used to calculate the dynamical critical exponent for homogeneous and disordered Ising-like systems.
We present a novel iterative algorithm for approximating the linear least squares solution with low complexity. After a motivation of the algorithm we discuss the algorithm's properties including its complexity, and we present theoretical…
In the theory and practice of inverse problems for partial differential equations (PDEs) much attention is paid to the problem of the identification of coefficients from some additional information. This work deals with the problem of…
The existence of a formal particular solution (family of solutions) of oscillating type under certain conditions has been proved for the quasi-linear ordinary differential equations system. The asymptotic nature of this solution (the family…
We develop efficient asymptotic-preserving time discretization schemes to solve the disparate mass kinetic system of a binary gas or plasma in the "relaxation time scale" relevant to the epochal relaxation phenomenon. Since the resulting…
A novel method, connecting the space of solutions of a linear differential equation, of arbitrary order, to the space of monomials, is used for exploring the algebraic structure of the solution space. Apart from yielding new expressions for…
We present and implement two algorithms for analytic asymptotic evaluation of the marginal likelihood of data given a Bayesian network with hidden nodes. As shown by previous work, this evaluation is particularly hard for latent Bayesian…
We study how to identify a class of continuous-time nonlinear systems defined by an ordinary differential equation affine in the unknown parameter. We define a notion of asymptotic consistency as $(n, h) \to (\infty, 0)$, and we achieve it…
In this paper we propose an algorithm for the numerical solution of arbitrary differential equations of fractional order. The algorithm is obtained by using the following decomposition of the differential equation into a system of…
In this paper cycles for asymptotic solutions for Heckman-Opdam hypergeometric system of type $A_n$ are described. Cycles are enumerated by elements of symmetric group. Leading asymptotic and leading coefficient are calculated. Value of…