相关论文: Solving the Selesnick-Burrus Filter Design Equatio…

Uncertainty Quantification for nonlinear hyperbolic problems becomes a challenging task in the vicinity of shocks. Standard intrusive methods lead to oscillatory solutions and can result in non-hyperbolic moment systems. The intrusive…

Global polynomial optimization is an important tool across applied mathematics, with many applications in operations research, engineering, and physical sciences. In various settings, the polynomials depend on external parameters that may…

We describe a novel iterative strategy for Kohn-Sham density functional theory calculations aimed at large systems (> 1000 electrons), applicable to metals and insulators alike. In lieu of explicit diagonalization of the Kohn-Sham…

We present an algebraic algorithm for quantum state tomography that leverages measurements of certain observables to estimate structured entries of the underlying density matrix. Under low-rank assumptions, the remaining entries can be…

Physics-informed neural operators have emerged as a powerful paradigm for solving parametric partial differential equations (PDEs), particularly in the aerospace field, enabling the learning of solution operators that generalize across…

In this paper, we consider Burgers' equation with uncertain boundary and initial conditions. The polynomial chaos (PC) approach yields a hyperbolic system of deterministic equations, which can be solved by several numerical methods. Here,…

$f,g_1,...,g_m$ be elements of the polynomial ring $\mathbb{R}[x_1,...,x_n]$. The paper deals with the general problem of computing a lower bound for $f$ on the subset of $\mathbb{R}^n$ defined by the inequalities $g_i\ge 0$, $i=1,...,m$.…

We present a new algorithm for solving a polynomial program P based on the recent "joint + marginal" approach of the first author for, parametric optimization. The idea is to first consider the variable x1 as a parameter and solve the…

Linear programming (polynomial) techniques are used to obtain lower and upper bounds for the potential energy of spherical designs. This approach gives unified bounds that are valid for a large class of potential functions. Our lower bounds…

When designing multispectral imaging systems for classifying different spectra it is necessary to choose a small number of filters from a set with several hundred different ones. Tackling this problem by full search leads to a tremendous…

We compare algorithms for global optimization of polynomial functions in many variables. It is demonstrated that existing algebraic methods (Gr\"obner bases, resultants, homotopy methods) are dramatically outperformed by a relaxation…

With the emergence of mixed precision capabilities in hardware, iterative refinement schemes for solving linear systems $Ax=b$ have recently been revisited and reanalyzed in the context of three or more precisions. These new analyses show…

There are several efficient methods to solve linear interval polynomial systems in the context of interval computations, however, the general case of interval polynomial systems is not yet covered as well. In this paper we introduce a new…

This study reports on the design of small footprint, integrated polarization filters based on engineered photonic lattices. Using a rods-in-air lattice as a basis for a TE filter and a holes-in-slab lattice for the analogous TM filter, we…

FIR (finite impulse response) digital filter design is a fundamental problem in signal processing. In particular, FIR approximation of analog filters (or systems) is ubiquitous not only in signal processing but also in digital…

Parametric linear systems are linear systems of equations in which some symbolic parameters, that is, symbols that are not considered to be candidates for elimination or solution in the course of analyzing the problem, appear in the…

In this paper we present an immersed weak Galerkin method for solving second-order elliptic interface problems on polygonal meshes, where the meshes do not need to be aligned with the interface. The discrete space consists of constants on…

In the General Position Subset Selection (GPSS) problem, the goal is to find the largest possible subset of a set of points such that no three of its members are collinear. If $s_{\mathrm{GPSS}}$ is the size of the optimal solution,…

The $k$-cut problem asks, given a connected graph $G$ and a positive integer $k$, to find a minimum-weight set of edges whose removal splits $G$ into $k$ connected components. We give the first polynomial-time algorithm with approximation…

High-order methods gain more and more attention in computational fluid dynamics. However, the potential advantage of these methods depends critically on the availability of efficient elliptic solvers. With spectral-element methods, static…