相关论文: Solving the Selesnick-Burrus Filter Design Equatio…
In this paper, a new filter model called set-membership Kalman filter for nonlinear state estimation problems was designed, where both random and unknown but bounded uncertainties were considered simultaneously in the discrete-time system.…
This paper proposes semi-discrete and fully discrete hybridizable discontinuous Galerkin (HDG) methods for the Burgers' equation in two and three dimensions. In the spatial discretization, we use piecewise polynomials of degrees $ k \ (k…
Consider a system of n polynomial equations and r polynomial inequations in n indeterminates of degree bounded by d with coefficients in a polynomial ring of s parameters with rational coefficients of bit-size at most $\sigma$. From the…
Starting from the results of Charles Fefferman and Janos Koll\'ar in \texit{Continuous Solutions of Linear Equations} [1], we adopt a new approach based on Fefferman's techniques of Glaeser refinement to show a more general result than the…
In two-phase image segmentation, convex relaxation has allowed global minimisers to be computed for a variety of data fitting terms. Many efficient approaches exist to compute a solution quickly. However, we consider whether the nature of…
A semiempirical parametric method is proposed for modeling three-dimensional (time-resolved) vibronic spectra of polyatomic molecules. The method is based on the use of the fragment approach in the formation of molecular models for excited…
Although Buchberger's algorithm, in theory, allows us to compute Gr\"obner bases over any field, in practice, however, the computational efficiency depends on the arithmetic of the ground field. Consider a field $K = \mathbb{Q}(\alpha)$, a…
In recent years, several powerful techniques have been developed to design {\em randomized} polynomial-space parameterized algorithms. In this paper, we introduce an enhancement of color coding to design deterministic polynomial-space…
Graphs are mathematical tools that can be used to represent complex real-world interconnected systems, such as financial markets and social networks. Hence, machine learning (ML) over graphs has attracted significant attention recently.…
This paper addresses the challenging problem of parameter estimation in bilinear systems under colored noise. A novel approach, termed B-PF-RLS, is proposed, combining a particle filter (PF) with a recursive least squares (RLS) estimator.…
This paper investigates beamforming-gain maximization for a fluid reconfigurable intelligent surface (FRIS)-assisted downlink system, where each active port applies a finite-resolution unit-modulus phase selected from a discrete codebook.…
In this paper, novel approaches are developed to explore the dynamics of motion in periodic orbits near libration points in cislunar space using the Differential Algebra (DA) framework. The Circular Restricted Three-Body Problem (CR3BP)…
We study the ideal generated by polynomials vanishing on a semialgebraic set and propose an algorithm to calculate the generators, which is based on some techniques of the cylindrical algebraic decomposition. By applying these, polynomial…
A new efficient algorithm is proposed for factoring polynomials over an algebraic extension field. The extension field is defined by a polynomial ring modulo a maximal ideal. If the maximal ideal is given by its Groebner basis, no extra…
The polynomial method from circuit complexity has been applied to several fundamental problems and obtains the state-of-the-art running times. As observed in [Alman and Williams, STOC 2017], almost all applications of the polynomial method…
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…
The paper develops the method for construction of the families of particular solutions to the nonlinear Partial Differential Equations (PDE) without relation to the complete integrability. Method is based on the specific link between…
We consider integer and linear programming problems for which the linear constraints exhibit a (recursive) block-structure: The problem decomposes into independent and efficiently solvable sub-problems if a small number of constraints is…
This paper presents a new filter for state-space models based on Bellman's dynamic-programming principle, allowing for nonlinearity, non-Gaussianity and degeneracy in the observation and/or state-transition equations. The resulting Bellman…
Given a generic semidefinite program, specified by matrices with rational entries, each coordinate of its optimal solution is an algebraic number. We study the degree of the minimal polynomials of these algebraic numbers. Geometrically,…