Related papers: On the Computation of 2-Dimensional Recurrence Equ…
In this paper, we present a new algorithm for computing the linear recurrence relations of multi-dimensional sequences. Existing algorithms for computing these relations arise in computational algebra and include constructing structured…
We consider two kinds of problems: the computation of polynomial and rational solutions of linear recurrences with coefficients that are polynomials with integer coefficients; indefinite and definite summation of sequences that are…
We are concerned with the monic orthogonal polynomials with respect to a singularly perturbed Laguerre-type weight. By using the ladder operator approach, we derive a complicated system of nonlinear second-order difference equations…
If the phase retrieval problem can be solved by a method similar to that of solving a system of linear equations under the context of FFT, the time complexity of computer based phase retrieval algorithm would be reduced. Here I present such…
We consider a two dimensional extension of the so-called linearizable mappings. In particular, we start from the Heideman-Hogan recurrence, which is known as one of the linearizable Somos-like recurrences, and introduce one of its two…
In this work we describe a fast and stable algorithm for the computation of the orthogonal moments of an image. Indeed, orthogonal moments are characterized by a high discriminative power, but some of their possible formulations are…
In this paper, we develop algorithms for computing the recurrence coefficients corresponding to multiple orthogonal polynomials on the step-line. We reformulate the problem as an inverse eigenvalue problem, which can be solved using…
A short review of the method for the tensor reduction of Feynman integrals based on recurrence relations with respect to space-time dimension d- is given. A solution of the difference equation with respect to d for the n - point one-loop…
We establish a simple recurrence formula for the number $Q_g^n$ of rooted orientable maps counted by edges and genus. We also give a weighted variant for the generating polynomial $Q_g^n(x)$ where $x$ is a parameter taking the number of…
Methods for the reduction of the complexity of computational problems are presented, as well as their connections to renormalization, scaling, and irreversible statistical mechanics. Several statistically stationary cases are analyzed; for…
New iterative methods for solving linear equations are presented that are easy to use, generalize good existing methods, and appear to be faster. The new algorithms mix two kinds of linear recurrence formulas. Older methods have either high…
The aim of our paper is to formulate and solve problems concerning multitime multiple recurrence equations. We discuss in detail the generic properties and the existence and uniqueness of solutions. Among the general things, we discuss in…
We establish a polynomial recursion formula for linear Hodge integrals. It is obtained as the Laplace transform of the cut-and-join equation for the simple Hurwitz numbers. We show that the recursion recovers the Witten-Kontsevich theorem…
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…
Every classical orthogonal polynomial system $p_n(x)$ satisfies a three-term recurrence relation of the type \[ p_{n+1}(x)=(A_nx+B_n)p_n(x)-C_np_{n-1}(x)~ (n=0,1,2,\ldots, p_{-1}\equiv 0), \] with $C_nA_nA_{n-1}>0$. Moreover, Favard's…
In this paper, we propose and analyze a fast two-point gradient algorithm for solving nonlinear ill-posed problems, which is based on the sequential subspace optimization method. A complete convergence analysis is provided under the…
The often elusive Poincar\'e recurrence can be witnessed in a completely separable system. For such systems, the problem of recurrence reduces to the classic mathematical problem of simultaneous Diophantine approximation of multiple…
In this paper we give efficient algorithms for computing second-, third-, and fourth-order linear recurrences. We also present an algorithm scheme for computing terms with the indices $N,\ldots,N+n-1$ of an $n$th-order linear recurrence.…
For the constrained 2-means problem, we present a $O\left(dn+d({1\over\epsilon})^{O({1\over \epsilon})}\log n\right)$ time algorithm. It generates a collection $U$ of approximate center pairs $(c_1, c_2)$ such that one of pairs in $U$ can…
In this paper we obtain an algorithm towards solving the two-dimensional moment problem. This algorithm gives the necessary and sufficient conditions for the solvability of the moment problem. It is shown that all solutions of the moment…