Related papers: An algorithm to approximate the real trilogarithm …
We report on the implementation of an algorithm for computing the set of all regular triangulations of finitely many points in Euclidean space. This algorithm, which we call down-flip reverse search, can be restricted, e.g., to computing…
We introduce data structures and algorithms to count numerical inaccuracies arising from usage of floating numbers described in IEEE 754. Here we describe how to estimate precision for some collection of functions most commonly used for…
Approximate computing methods have shown great potential for deep learning. Due to the reduced hardware costs, these methods are especially suitable for inference tasks on battery-operated devices that are constrained by their power budget.…
We propose a probabilistic setting in which we study the probability law of the Rajaraman and Ullman \textit{RU} algorithm and a modified version of it denoted by \textit{RUM}. These algorithms aim at estimating the similarity index between…
The alpha complex, a subset of the Delaunay triangulation, has been extensively used as the underlying representation for biomolecular structures. We propose a GPU-based parallel algorithm for the computation of the alpha complex, which…
The overall problem addressed in this paper is the long-standing problem of program correctness, and in particular programs that describe systems of parallel executing processes. We propose a new method for proving correctness of parallel…
Our paper presents an attempt to axiomatise signal processing. Our long-term goal is to formulate signal processing algorithms for an ideal world of exact computation and prove properties about them, then interpret these ideal formulations…
The paper gives a systematic study of the approximate versions of three greedy-type algorithms that are widely used in convex optimization. By approximate version we mean the one where some of evaluations are made with an error. Importance…
In this paper, we present experimental algorithms for solving the dualization problem. We present the results of extensive experimentation comparing the execution time of various algorithms.
This paper proposes a combination of a hybrid CPU--GPU and a pure GPU software implementation of a direct algorithm for solving shifted linear systems $(A - \sigma I)X = B$ with large number of complex shifts $\sigma$ and multiple…
We survey key techniques and results from approximation theory in the context of uniform approximations to real functions such as e^{-x}, 1/x, and x^k. We then present a selection of results demonstrating how such approximations can be used…
The (1,2)-TSP is a special case of the TSP where each edge has cost either 1 or 2. In this paper we give a lower bound of $\frac{3}{2}$ for the approximation ratio of the 2-Opt algorithm for the (1,2)-TSP. Moreover, we show that the 3-Opt…
We present a new approximation algorithm for the minimum 2-edge-connected spanning subgraph problem. Its approximation ratio is $\frac{4}{3}$, which matches the current best ratio. The approximation ratio of the algorithm is $\frac{6}{5}$…
The Parareal algorithm is used to solve time-dependent problems considering multiple solvers that may work in parallel. The key feature is a initial rough approximation of the solution that is iteratively refined by the parallel solvers. We…
Multi-socket multi-core servers are used for solving some of the important problems in computing. Remote DRAM accesses can impact performance of certain applications running on such servers. This paper presents a new near linear operating…
Micro-macro models provide a powerful tool to study the relationship between microscale mechanisms and emergent macroscopic behavior. However, the detailed microscopic modeling may require tracking and evolving a high-dimensional…
Many problems in machine learning can be solved by rounding the solution of an appropriate linear program (LP). This paper shows that we can recover solutions of comparable quality by rounding an approximate LP solution instead of the ex-…
Rational minimax approximation of real functions on real intervals is an established topic, but when it comes to complex functions or domains, there appear to be no algorithms currently in use. Such a method is introduced here, the {\em…
The complex-step derivative approximation is a numerical differentiation technique that can achieve analytical accuracy, to machine precision, with a single function evaluation. In this letter, the complex-step derivative approximation is…
In this paper we propose an algorithm for the approximate k-Nearest-Neighbors problem. According to the existing researches, there are two kinds of approximation criterion. One is the distance criteria, and the other is the recall criteria.…