相关论文: Spectral approach to linear programming bounds on …

The lower and upper bound of any given algorithm is one of the most crucial pieces of information needed when evaluating the computational effectiveness for said algorithm. Here a novel method of Boolean Algebraic Programming for symbolic…

In this paper, we study regression problems over a separable Hilbert space with the square loss, covering non-parametric regression over a reproducing kernel Hilbert space. We investigate a class of spectral/regularized algorithms,…

We introduce linear programs encoding regular expressions of finite languages. We show that, given a language, the optimum value of the associated linear program is a lower bound on the size of any regular expression of the language.…

In many high-dimensional problems,polynomial-time algorithms fall short of achieving the statistical limits attainable without computational constraints. A powerful approach to probe the limits of polynomial-time algorithms is to study the…

We prove a linear bound on the average total curvature of the central path of linear programming theory in terms on the number of independent variables of the primal problem, and independent on the number of constraints.

Lienard systems are very important mathematical models describing oscillatory processes arising in applied sciences. In this paper, we study polynomial Lienard systems of arbitrary degree on the plane, and develop a new method to obtain a…

Let $C$ be a binary code of length $n$ with distances $0<d_1<\cdots<d_s\le n$. In this note we prove a general upper bound on the size of $C$ without any restriction on the distances $d_i$. The bound is asymptotically optimal.

Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…

We study sequences of linear or affine codes with uniform weight spectrum, i.e., a part of codewords with any fixed weight tends to zero. It is proved that a sequence of linear codes has a uniform weight spectrum if the number of vectors…

For an unbounded operator $S$ on a Banach space the existence of invariant subspaces corresponding to its spectrum in the left and right half-plane is proved. The general assumption on $S$ is the uniform boundedness of the resolvent along…

We present some upper and lower bounds for the numerical radius of a bounded linear operator defined on complex Hilbert space, which improves on the existing upper and lower bounds. We also present an upper bound for the spectral radius of…

We derive and investigate lower bounds for the potential energy of finite spherical point sets (spherical codes). Our bounds are optimal in the following sense -- they cannot be improved by employing polynomials of the same or lower degrees…

The aims of this article are two-fold. First, we give a geometric characterization of the optimal basic solutions of the general linear programming problem (no compactness assumptions) and provide a simple, self-contained proof of it…

Detectability of failures of linear programming (LP) decoding and the potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the underlying LP problem. In this paper, we…

We analyze randomized matrix-free quadrature algorithms for spectrum and spectral sum approximation. The algorithms studied include the kernel polynomial method and stochastic Lanczos quadrature, two widely used methods for these tasks. Our…

We prove upper bounds on the graph diameters of polytopes in two settings. The first is a worst-case bound for polytopes defined by integer constraints in terms of the height of the integers and certain subdeterminants of the constraint…

In this paper we generalize N-fold integer programs and two-stage integer programs with N scenarios to N-fold 4-block decomposable integer programs. We show that for fixed blocks but variable N, these integer programs are polynomial-time…

We study the problem of compression for the purpose of similarity identification, where similarity is measured by the mean square Euclidean distance between vectors. While the asymptotical fundamental limits of the problem - the minimal…

The long-standing problem of minimal projections is addressed from a computational point of view. Techniques to determine bounds on the projection constants of univariate polynomial spaces are presented. The upper bound, produced by a…

Observable convolutional codes defined over Zpr with the Predictable Degree Property admit minimal input/state/output representations that preserve structural properties under scalar restriction. We make use of this fact to present…