Related papers: On the use of the Infinity Computer architecture t…
This paper is concerned with the approximation of solutions to a class of second order non linear abstract differential equations. The finite-dimensional approximate solutions of the given system are built with the aid of the projection…
The well-known Turing machine is an example of a theoretical digital computer, and it was the logical basis of constructing real electronic computers. In the present paper we propose an alternative, namely, by formalising arithmetic…
Renewed interest in mixed-precision algorithms has emerged due to growing data capacity and bandwidth concerns, as well as the advancement of GPUs, which enable significant speedup for low precision arithmetic. In light of this, we propose…
In this paper, we propose an approach for computing invariant sets of discrete-time nonlinear systems by lifting the nonlinear dynamics into a higher dimensional linear model. In particular, we focus on the \emph{maximal admissible…
We consider linear programming (LP) problems in infinite dimensional spaces that are in general computationally intractable. Under suitable assumptions, we develop an approximation bridge from the infinite-dimensional LP to tractable finite…
Max-infinitely divisible (max-id) processes play a central role in extreme-value theory and include the subclass of all max-stable processes. They allow for a constructive representation based on the pointwise maximum of random functions…
The increasing difficulty in continued development of digital electronic logic has led to a renewed interest in alternative approaches. Oscillatory computing is one such approach that leverages alternative physical systems and computation…
Numerical simulations are ubiquitous in mathematics and computational science. Several industrial and clinical applications entail modeling complex multiphysics systems that evolve over a variety of spatial and temporal scales. This study…
Abstract argumentation frameworks (AFs) provide a formal setting to analyze many forms of reasoning with conflicting information. While the expressiveness of general infinite AFs make them a tempting tool for modeling many kinds of…
The design of embedded control systems is mainly done with model-based tools such as Matlab/Simulink. Numerical simulation is the central technique of development and verification of such tools. Floating-point arithmetic, that is well-known…
Input-affine dynamical systems often arise in control and modeling scenarios, such as the data-driven case when state-derivative observations are recorded under bounded noise. Common tasks in system analysis and control include optimal…
The need to describe abrupt changes or response of nonlinear systems to impulsive stimuli is ubiquitous in applications. Also the informal use of infinitesimal and infinite quantities is still a method used to construct idealized but…
Modern computer architectures support low-precision arithmetic, which present opportunities for the adoption of mixed-precision algorithms to achieve high computational throughput and reduce energy consumption. As a growing number of…
We propose a novel solution framework for inverse mixed-integer optimization based on analytic center concepts from interior point methods. We characterize the optimality gap of a given solution, provide structural results, and propose…
Recent research has shown that large language models (LLMs) can utilize low-precision floating point (FP) quantization to deliver high efficiency while maintaining original model accuracy. In particular, recent works have shown the…
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…
An improvement on precision of recursive function simulation in IEEE floating point standard is presented. It is shown that the average of rounding towards negative infinite and rounding towards positive infinite yields a better result than…
Nonlinear dynamics and pattern formation in the systems with quadratic nonlinearity is computed symbolically by specially developed MATHEMATICA package. A Web interface for the presented methods is developed, which turns the implementations…
Low-cost embedded processors such as the ESP32 (Xtensa LX6, 32-bit dual-core, 240 MHz) are increasingly used in edge computing applications that require real-time physical simulation, sensor fusion, and control systems. Although the ESP32…
In this paper, we address the problem of computing the maximal admissible robust positive invariant (MARPI) set for discrete-time linear time-varying systems with parametric uncertainties and additive disturbances. The system state and…