相关论文: Efficiently Computing Minimal Sets of Critical Pai…

This paper introduces some efficient initials for a well-known algorithm (an inverse iteration) for computing the maximal eigenpair of a class of real matrices. The initials not only avoid the collapse of the algorithm but are also…

Border bases can be considered to be the natural extension of Gr\"obner bases that have several advantages. Unfortunately, to date the classical border basis algorithm relies on (degree-compatible) term orderings and implicitly on reduced…

This paper proposes a novel low complexity joint bit and power suboptimal allocation algorithm for multicarrier systems operating in fading environments. The algorithm jointly maximizes the throughput and minimizes the transmitted power,…

Motivated by genome-wide association studies, we consider a standard linear model with one additional random effect in situations where many predictors have been collected on the same subjects and each predictor is analyzed separately.…

Filters are the basic and most important blocks of most signal processing applications. In many applications, a group of parallel filters are used as filter banks. Parallel filter banks naturally require much more computations. Especially…

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…

Gr\"obner bases can be used for computing the Hilbert basis of a numerical submonoid. By using these techniques, we provide an algorithm that calculates a basis of a subspace of a finite-dimensional vector space over a finite prime field…

Widely used Lagrangian numerical codes that compute the physical interaction with neighbouring resolution elements (particles), duplicate the calculation of the interaction between pairs of particles. We developed an algorithm that reduces…

Efficient computation of shortest cycles which form a homology basis under $\mathbb{Z}_2$-additions in a given simplicial complex $\mathcal{K}$ has been researched actively in recent years. When the complex $\mathcal{K}$ is a weighted graph…

In this paper we introduce a binomial ideal derived from a binary linear code. We present some applications of a Gr\"obner basis of this ideal with respect to a total degree ordering. In the first application we give a decoding method for…

Importance sampling has been reported to produce algorithms with excellent empirical performance in counting problems. However, the theoretical support for its efficiency in these applications has been very limited. In this paper, we…

In the context of modeling biological systems, it is of interest to generate ideals of points with a unique reduced Groebner basis, and the first main goal of this paper is to identify classes of ideals in polynomial rings which share this…

Due to the highly non-convex nature of large-scale robust parameter estimation, avoiding poor local minima is challenging in real-world applications where input data is contaminated by a large or unknown fraction of outliers. In this paper,…

We present a number of novel algorithms, based on mathematical optimization formulations, in order to solve a homogeneous multiprocessor scheduling problem, while minimizing the total energy consumption. In particular, for a system with a…

Efficiently implementing Clifford circuits is crucial for quantum error correction and quantum algorithms. Linear reversible circuits, equivalent to circuits composed of CNOT gates, have important applications in classical computing. In…

We describe an algorithm for arbitrary-precision computation of the elementary functions (exp, log, sin, atan, etc.) which, after a cheap precomputation, gives roughly a factor-two speedup over previous state-of-the-art algorithms at…

We investigate the application of syzygies for efficiently computing (finite) Pommaret bases. For this purpose, we first describe a non-trivial variant of Gerdt's algorithm to construct an involutive basis for the input ideal as well as an…

Since simulating quantum computers requires exponentially more classical resources, efficient algorithms are extremely helpful. We analyze algorithms that create single qubit and specific controlled qubit matrix representations of gates.…

Optimization of circuits is an essential task for both quantum and classical computers to improve their efficiency. In contrast, classical logic optimization is known to be difficult, and a lot of heuristic approaches have been developed so…

In this paper the problem of finding the sparsest (i.e., minimum cardinality) critical $k$-tuple including one arbitrarily specified measurement is considered. The solution to this problem can be used to identify weak points in the…