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

We propose a new polynomial-time algorithm for linear programming. We further extend the ideas used in this new linear programming algorithm for nonlinear programming problems. The new algorithm is based on the idea of treating the…

For three decades, carrier-phase observations have been used to obtain the most accurate location estimates using global navigation satellite systems (GNSS). These estimates are computed by minimizing a nonlinear mixed-integer least-squares…

In dual-function radar-communication (DFRC) systems the probing signal contains information intended for the communication users, which makes that information vulnerable to eavesdropping by the targets. We study the security of a DFRC…

The sinc function is often used as the basis for the design of discrete linear-phase FIR filters. However the Fourier transform of the truncated sinc function exhibits ripple in the pass band due to the Gibbs phenomenon. This paper…

Our goal in this paper is the robust design of filters acting on signals observed over graphs subject to small perturbations of their edges. The focus is on developing a method to identify spectral and polynomial graph filters that can…

Para-Hermitian polynomial matrices obtained by matrix spectral factorization lead to functions useful in control theory systems, basis functions in numerical methods or multiscaling functions used in signal processing. We introduce a fast…

Here we study theoretically and compare experimentally an efficient method for solving systems of algebraic equations, where the matrix comes from the discretization of a fractional diffusion operator. More specifically, we focus on…

An efficient technique to solve precision problems consists in using exact computations. For geometric predicates, using systematically expensive exact computations can be avoided by the use of filters. The predicate is first evaluated…

Stochastic Barrier Functions (SBFs) certify the safety of stochastic systems by formulating a functional optimization problem, which state-of-the-art methods solve using Sum-of-Squares (SoS) polynomials. This work focuses on polynomial SBFs…

Polynomial partitioning techniques have recently led to improved geometric data structures for a variety of fundamental problems related to semialgebraic range searching and intersection searching in 3D and higher dimensions (e.g., see…

A new robust algorithm for the numerical computation of biarcs, i.e. $G^1$ curves composed of two arcs of circle, is presented. Many algorithms exist but are based on geometric constructions, which must consider many geometrical…

We introduce a new perspective and mathematical model for the generalized frequency division multiplexing (GFDM) to analyze the effect of self-interferences and remove their detrimental impacts. Using this model, we express the GFDM signal…

In this work, inspired by the study of semidefinite programming for block-diagonalizing matrix *-algebras, we propose an algorithm that can find the algebraic structure of decoherence-free subspaces (DFS's) for a given noisy quantum…

This paper focuses on the design of multiplier-less decimation filters suitable for oversampled digital signals. The aim is twofold. On one hand, it proposes an optimization framework for the design of constituent decimation filters in a…

The problem of constrained finite impulse response (FIR) filter design is central to signal processing and arises in a variety of disciplines. This paper surveys the design of such filters using Projection onto convex sets (POCS) and…

We present an effective method for computing parametric primary decomposition via comprehensive Gr\"obner systems. In general, it is very difficult to compute a parametric primary decomposition of a given ideal in the polynomial ring with…

We demonstrate applications of algebraic techniques that optimize and certify polynomial inequalities to problems of interest in the operations research and transportation engineering communities. Three problems are considered: (i) wireless…

Local polynomial smoothing is a widespread technique in data analysis, and Savitzky-Golay (SG) filters are one of its most well-known realizations. In real settings, the effectiveness of SG filtering depends critically on proper tuning of…

We present two methods to algorithmically compute both least and greatest solutions of polynomial equation systems over absorptive semirings (with certain completeness and continuity assumptions), such as the tropical semiring. Both methods…

Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…