Related papers: Exploiting Binary Floating-Point Representations f…

Floating point error is an inevitable drawback of embedded systems implementation. Computing rigorous upper bounds of roundoff errors is absolutely necessary to the validation of critical software. This problem is even more challenging when…

Floating point division, even though being an infrequent operation in the traditional sense, is indis- pensable when it comes to a range of non-traditional applications such as K-Means Clustering and QR Decomposition just to name a few. In…

We propose an implementation of symplectic implicit Runge-Kutta schemes for highly accurate numerical integration of non-stiff Hamiltonian systems based on fixed point iteration. Provided that the computations are done in a given floating…

Floating-point round-off errors are ubiquitous in numerically intensive programs arising in fields such as scientific computing and optimization. As floating-point errors potentially lead to unexpected and catastrophic program failures, one…

In basic computational physics classes, students often raise the question of how to compute a number that exceeds the numerical limit of the machine. While technique of avoiding overflow/underflow has practical application in the electrical…

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…

In this paper, we study binary constrained codes that are resilient to bit-flip errors and erasures. In our first approach, we compute the sizes of constrained subcodes of linear codes. Since there exist well-known linear codes that achieve…

The Bin Packing Problem is one of the most important problems in discrete optimization, as it captures the requirements of many real-world problems. Because of its importance, it has been approached with the main theoretical and practical…

We propose a scheme for reduced-precision representation of floating point data on a continuum between IEEE-754 floating point types. Our scheme enables the use of lower precision formats for a reduction in storage space requirements and…

Iterative algorithms aimed at solving some problems are discussed. For certain problems, such as finding a common point in the intersection of a finite number of convex sets, there often exist iterative algorithms that impose very little…

Probabilistic model checking computes probabilities and expected values related to designated behaviours of interest in Markov models. As a formal verification approach, it is applied to critical systems; thus we trust that probabilistic…

Many interesting and fundamentally practical optimization problems, ranging from optics, to signal processing, to radar and acoustics, involve constraints on the Fourier transform of a function. It is well-known that the {\em fast Fourier…

Binary optimization, a representative subclass of discrete optimization, plays an important role in mathematical optimization and has various applications in computer vision and machine learning. Usually, binary optimization problems are…

Constrained quasiconvex optimization problems appear in many fields, such as economics, engineering, and management science. In particular, fractional programming, which models ratio indicators such as the profit/cost ratio as fractional…

Given the current trend of increasing size and complexity of machine learning architectures, it has become of critical importance to identify new approaches to improve the computational efficiency of model training. In this context, we…

We introduce an alternative approach for constrained mathematical programming problems. It rests on two main aspects: an efficient way to compute optimal solutions for unconstrained problems, and multipliers regarded as variables for a…

One of the major promises of quantum computing is the realization of SIMD (single instruction - multiple data) operations using the phenomenon of superposition. Since the dimension of the state space grows exponentially with the number of…

Simulation-based verification algorithms can provide formal safety guarantees for nonlinear and hybrid systems. The previous algorithms rely on user provided model annotations called discrepancy function, which are crucial for computing…

IIn computational geometry, the construction of essential primitives like convex hulls, Voronoi diagrams and Delaunay triangulations require the evaluation of the signs of determinants, which are sums of products. The same signs are needed…

This paper develops methods of distributed Bayesian hypothesis tests for fault detection and diagnosis that are based on belief propagation and optimization in graphical models. The main challenges in developing distributed statistical…