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We introduce a new technique for solving uni-parametric versions of linear programs, convex quadratic programs, and linear complementarity problems in which a single parameter is permitted to be present in any of the input data. We…

Boundary value problems involving elliptic PDEs such as the Laplace and the Helmholtz equations are ubiquitous in mathematical physics and engineering. Many such problems can be alternatively formulated as integral equations that are…

In this brief, we discuss the implementation of a third order semi-implicit differentiator as a complement of the recent work by the author that proposes an interconnected semi-implicit Euler double differentiators algorithm through Taylor…

In this article, we propose an interval constraint programming method for globally solving catalog-based categorical optimization problems. It supports catalogs of arbitrary size and properties of arbitrary dimension, and does not require…

We present a batched first-order method for solving multiple linear programs in parallel on GPUs. Our approach extends the primal-dual hybrid gradient algorithm to efficiently solve batches of related linear programming problems that arise…

This paper presents a novel parallel-in-time algorithm able to compute time-periodic solutions of problems where the period is not given. Exploiting the idea of the multiple shooting method, the proposed approach calculates the initial…

Machine learning has achieved dramatic success over the past decade, with applications ranging from face recognition to natural language processing. Meanwhile, rapid progress has been made in the field of quantum computation including…

The concept of a universal algorithm is discussed. Examples of this kind of algorithms are presented. Software implementations of such algorithms in C++ type languages are discussed together with means that provide for computations with an…

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…

Based on the partition of parameter space, two algorithms for computing the rational univariate representation of zero-dimensional ideals with parameters are presented in the paper. Unlike the rational univariate representation of…

We present an open-source Julia-based software toolkit for solving the phase problem using dual-space iterative algorithms. The toolkit is specifically designed for aperiodic crystals and quasicrystals, supporting general space group…

In this study, perturbation-iteration algorithm, namely PIA, is applied to solve some types of system of fractional differential equations (FDEs) for the first time. To illustrate the efficiency of the method, numerical solutions are…

Parametric linear programming is central in polyhedral computations and in certain control applications.We propose a task-based scheme for parallelizing it, with quasi-linear speedup over large problems.

We propose a primal--dual technique that applies to infinite dimensional equality constrained problems, in particular those arising from optimal control. As an application of our general framework, we solve a control-constrained double…

The fusion research facility ITER is currently being assembled to demonstrate that fusion can be used for industrial energy production, while several other programmes across the world are also moving forward, such as EU-DEMO, CFETR, SPARC…

In this paper we present BilevelJuMP, a new Julia package to support bilevel optimization within the JuMP framework. The package is a Julia library that enables the user to describe both upper and lower-level optimization problems using the…

This paper is devoted to computational algorithms designed to describe the classical Ising magnet in some specific cases when an additional macroscopic restriction in form of constant charge density exists in the system. We developed and…

Technical computing is a challenging application area for programming languages to address. This is evinced by the unusually large number of specialized languages in the area (e.g. MATLAB, R), and the complexity of common software stacks,…

Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…

As has been shown in our previous work, the parallel-in-time direct inverse (ParaDIn) method introduced by Yamaleev and Paudel in (arXiv: 2406.00878v1, 2024) imposes some constraint on the maximum number of time levels, $N_t$, that can be…