Related papers: Polynomial Invariant Generation for Floating-Point…
Consider a polynomial optimisation problem, whose instances vary continuously over time. We propose to use a coordinate-descent algorithm for solving such time-varying optimisation problems. In particular, we focus on relaxations of…
The search for multivariate quadrature rules of minimal size with a specified polynomial accuracy has been the topic of many years of research. Finding such a rule allows accurate integration of moments, which play a central role in many…
FP-Growth algorithm is a Frequent Pattern Min- ing (FPM) algorithm that has been extensively used to study correlations and patterns in large scale datasets. While several researchers have designed distributed memory FP-Growth algorithms,…
The amounts of data that need to be transmitted, processed, and stored by the modern deep neural networks have reached truly enormous volumes in the last few years calling for the invention of new paradigms both in hardware and software…
In this paper, we propose a mixed-precision convolution unit architecture which supports different integer and floating point (FP) precisions. The proposed architecture is based on low-bit inner product units and realizes higher precision…
This work aims to introduce the framework of polynomial optimization theory to solve fractional polynomial problems (FPPs). Unlike other widely used optimization frameworks, the proposed one applies to a larger class of FPPs, not…
We study the numerical integration problem for functions with infinitely many variables. The function spaces of integrands we consider are weighted reproducing kernel Hilbert spaces with norms related to the ANOVA decomposition of the…
Due to limited resources and fast economic growth, designing optimal transportation road networks with traffic simulation and validation in a cost-effective manner is vital for developing countries, where extensive manual testing is…
Dealing with multi-objective problems by using generation methods has some interesting advantages since it provides the decision-maker with the complete information about the set of non-dominated points (Pareto front) and a clear overview…
In this paper we study a class of dynamical systems generated by iterations of multivariate polynomials and estimate the degreegrowth of these iterations. We use these estimates to bound exponential sums along the orbits of these dynamical…
Provably correct software is one of the key challenges of our software-driven society. Program synthesis -- the task of constructing a program satisfying a given specification -- is one strategy for achieving this. The result of this task…
Ootomo, Ozaki, and Yokota [Int. J. High Perform. Comput. Appl., 38 (2024), p. 297-313] have proposed a strategy to recast a floating-point matrix multiplication in terms of integer matrix products. The factors A and B are split into integer…
In computer aided geometric design a polynomial is usually represented in Bernstein form. This paper presents a family of compensated algorithms to accurately evaluate a polynomial in Bernstein form with floating point coefficients. The…
Multi-objective integer or mixed-integer programming problems typically have disconnected feasible domains, making the task of constructing an approximation of the Pareto front challenging. The present paper shows that certain algorithms…
Block Floating Point (BFP) arithmetic is currently seeing a resurgence in interest because it requires less power, less chip area, and is less complicated to implement in hardware than standard floating point arithmetic. This paper explores…
In recursive state estimation, numerical error can play a major role in an algorithm's overall performance and reliability. Roundoff errors due to finite precision arithmetic can violate theoretical guarantees, leading to asymmetric and…
We show that one can approximate the least fixed point solution for a multivariate system of monotone probabilistic polynomial equations in time polynomial in both the encoding size of the system of equations and in log(1/\epsilon), where…
We explore a multiple-stage variant of the min-max robust selection problem with budgeted uncertainty that includes queries. First, one queries a subset of items and gets the exact values of their uncertain parameters. Given this…
Optimal control of turbulent mixed-convection flows has attracted considerable attention from researchers. Numerical algorithms such as Genetic Algorithms (GAs) are powerful tools that allow to perform global optimization. These algorithms…
This paper develops a correspondence relating convex hulls of fractional functions with those of polynomial functions over the same domain. Using this result, we develop a number of new reformulations and relaxations for fractional…