Related papers: Obtaining Exact Value by Approximate Computations
The input to the distant representatives problem is a set of $n$ objects in the plane and the goal is to find a representative point from each object while maximizing the distance between the closest pair of points. When the objects are…
Many problems of theoretical and practical interest involve finding an optimum over a family of convex functions. For instance, finding the projection on the convex functions in $H^k(\Omega)$, and optimizing functionals arising from some…
The subset sum problem is known to be an NP-hard problem in the field of computer science with the fastest known approach having a run-time complexity of $O(2^{0.3113n})$. A modified version of this problem is known as the perfect sum…
We develop a complexity theory for approximate real computations. We first produce a theory for exact computations but with condition numbers. The input size depends on a condition number, which is not assumed known by the machine. The…
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…
How best to quantify the information of an object, whether natural or artifact, is a problem of wide interest. A related problem is the computability of an object. We present practical examples of a new way to address this problem. By…
This application for learning APPROXIMATION ALGORITHM has been designed in Java which will make user comfortable in learning the very complex subject "NP-Completeness" and the solution to NP-Complete problem using approximation algorithm.
Recent research has demonstrated that quantum computers can solve certain types of problems substantially faster than the known classical algorithms. These problems include factoring integers and certain physics simulations. Practical…
The proximal gradient algorithm has been popularly used for convex optimization. Recently, it has also been extended for nonconvex problems, and the current state-of-the-art is the nonmonotone accelerated proximal gradient algorithm.…
Approximate integer programming is the following: For a convex body $K \subseteq \mathbb{R}^n$, either determine whether $K \cap \mathbb{Z}^n$ is empty, or find an integer point in the convex body scaled by $2$ from its center of gravity…
Computing market equilibria is an important practical problem for market design, for example in fair division of items. However, computing equilibria requires large amounts of information (typically the valuation of every buyer for every…
In this review paper, we give a comprehensive overview of the large variety of approximation results for neural networks. Approximation rates for classical function spaces as well as benefits of deep neural networks over shallow ones for…
We consider list versions of sparse approximation problems, where unlike the existing results in sparse approximation that consider situations with unique solutions, we are interested in multiple solutions. We introduce these problems and…
Given the stringent requirements of energy efficiency for Internet-of-Things edge devices, approximate multipliers, as a basic component of many processors and accelerators, have been constantly proposed and studied for decades, especially…
We provide experimental evaluation of a number of known and new algorithms for approximate computation of Monroe's and Chamberlin-Courant's rules. Our experiments, conducted both on real-life preference-aggregation data and on synthetic…
In this paper we describe an algorithm for implicitizing rational hypersurfaces in case there exists at most a finite number of base points. It is based on a technique exposed in math.AG/0210096, where implicit equations are obtained as…
Emerging applications such as augmented reality and tactile Internet are compute-intensive and latency-sensitive, which hampers their running in constrained end devices alone or in the distant cloud. The stringent requirements of such…
Probabilistic graphical models have emerged as a powerful modeling tool for several real-world scenarios where one needs to reason under uncertainty. A graphical model's partition function is a central quantity of interest, and its…
Linear approximations of the AC power flow equations are of great significance for the computational efficiency of large-scale optimal power flow (OPF) problems. Put differently, the feasibility of the obtained solution is essential for…
Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…