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Related papers: Complex moment problem and recursive relations

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The two-dimensional moment problem consists of finding a positive Borel measure $\mu$ in $\mathbb{R}^2$ such that $\int_{\mathbb{R}^2} t_1^m t_2^n d\mu = s_{m,n}$, $m,n=0,1,2,...$, where $s_{m,n}$ are prescribed real constants (moments). We…

Classical Analysis and ODEs · Mathematics 2025-08-15 Sergey M. Zagorodnyuk

Novel classes of dynamical systems are introduced, including many-body problems characterized by nonlinear equations of motion of Newtonian type ("acceleration equals forces") which determine the motion of points in the complex plane. These…

Mathematical Physics · Physics 2016-01-20 Oksana Bihun , Francesco Calogero

We study the computational complexity of approximating general constrained Markov decision processes. Our primary contribution is the design of a polynomial time $(0,\epsilon)$-additive bicriteria approximation algorithm for finding optimal…

Data Structures and Algorithms · Computer Science 2025-02-12 Jeremy McMahan

A system of inhomogeneous second-order difference equations with linear parts given by noncommutative matrix coefficients are considered. Closed form of its solution is derived by means of newly defined delayed matrix sine/cosine using the…

Dynamical Systems · Mathematics 2025-02-28 Nazim I. Mahmudov

We consider a non-polynomial cubic spline to develop the classes of methods for the numerical solution of singularly perturbed two-point boundary value problems. The proposed methods are second and fourth order accurate and applicable to…

Numerical Analysis · Mathematics 2012-06-13 Islam Khan , Tariq Aziz

We investigate bicomplex Hamiltonian systems in the framework of an analogous version of the Schrodinger equation. Since in such a setting three different types of conjugates of bicomplex numbers appear, each is found to define in a natural…

Mathematical Physics · Physics 2015-11-23 Bijan Bagchi , Abhijit Banerjee

We consider certain systems of three linked simultaneous diagonal equations in ten variables with total degree exceeding five. By means of a complification argument, we obtain an asymptotic formula for the number of integral solutions of…

Number Theory · Mathematics 2021-06-09 Joerg Bruedern , Trevor D. Wooley

The trigonometric moment problem arises from the study of one-parameter families of centers in polynomial vector fields. It asks for the classification of the trigonometric polynomials $Q$ which are orthogonal to all powers of a…

Classical Analysis and ODEs · Mathematics 2011-09-21 Amelia Álvarez , José Luis Bravo , Colin Christopher

Single scale quantities, as anomalous dimensions and hard scattering cross sections, in renormalizable Quantum Field Theories are found to obey difference equations of finite order in Mellin space. It is often easier to calculate fixed…

High Energy Physics - Phenomenology · Physics 2009-12-10 J. Blümlein , M. Kauers , S. Klein , C. Schneider

We provide a randomized linear time approximation scheme for a generic problem about clustering of binary vectors subject to additional constrains. The new constrained clustering problem encompasses a number of problems and by solving it,…

Data Structures and Algorithms · Computer Science 2018-07-20 Fedor V. Fomin , Petr A. Golovach , Daniel Lokshtanov , Fahad Panolan , Saket Saurabh

We apply the theory of disconjugate linear recurrence relations to the study of irrational quantities in number theory. In particular, for an irrational number associated with solutions of three-term linear recurrence relations we show that…

Number Theory · Mathematics 2008-03-27 Angelo B. Mingarelli

This paper considers computing interior singular triplets corresponding to the singular values in some interval. Based on the concept of the complex moment-based parallel eigensolvers, in this paper, we propose a novel complex moment-based…

Numerical Analysis · Mathematics 2021-09-29 Akira Imakura , Tetsuya Sakurai

There has been a resurgence of interest in lower bounds whose truth rests on the conjectured hardness of well known computational problems. These conditional lower bounds have become important and popular due to the painfully slow progress…

Data Structures and Algorithms · Computer Science 2015-04-09 Raphael Clifford , Allan Grønlund , Kasper Green Larsen

Building on the blueprint from Goemans and Williamson (1995) for the Max-Cut problem, we construct a polynomial-time approximation algorithm for orthogonally constrained quadratic optimization problems. First, we derive a semidefinite…

Optimization and Control · Mathematics 2026-03-17 Ryan Cory-Wright , Jean Pauphilet

This paper is a continuation of our previous investigations on the truncated matrix trigonometric moment problem in Ukrainian Math. J., 2011, \textbf{63}, no. 6, 786-797, and Ukrainian Math. J., 2013, \textbf{64}, no. 8, 1199-1214. In this…

Functional Analysis · Mathematics 2015-05-19 Sergey M. Zagorodnyuk

We present a method for solving the general mixed constrained convex quadratic programming problem using an active set method on the dual problem. The approach is similar to existing active set methods, but we present a new way of solving…

Optimization and Control · Mathematics 2019-12-02 Mattias Fält , Pontus Giselsson

In this paper, we describe new methods to compute the radical (resp. real radical) of an ideal, assuming it complex (resp. real) variety is finite. The aim is to combine approaches for solving a system of polynomial equations with dual…

Algebraic Geometry · Mathematics 2011-12-21 Jean-Bernard Lasserre , Monique Laurent , Bernard Mourrain , Philipp Rostalski , Philippe Trébuchet

A direct numerical solution of the radiative transfer equation or any kinetic equation is typically expensive, since the radiative intensity depends on time, space and direction. An expansion in the direction variables yields an equivalent…

Mathematical Physics · Physics 2023-10-10 Benjamin Seibold , Martin Frank

The fibre theorem \cite{schm2003} for the moment problem on closed semi-algebraic subsets of $\R^d$ is generalized to finitely generated real unital algebras. A charaterization of moment functionals on the polynomial algebra…

Functional Analysis · Mathematics 2014-06-03 Konrad Schmüdgen

In this paper, we consider linear functionals defined on an unital commutative real algebra A and establish characterizations for moment functionals on compact sets of characters that depend only on the given functional. For example, we…

Functional Analysis · Mathematics 2025-12-09 Dragu Atanasiu