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Using exhaustion method and finite differences a new method to solve system of partial differential equations and is presented. This method allows design algorithm to solve linear and nonlinear systems in irregular domains. Applying this…
Given a first-order autonomous algebraic ordinary differential equation, we present a method for computing formal power series solutions by means of places. We provide an algorithm for computing a full characterization of possible initial…
In a previous paper, an implementable algorithm was introduced to compute discrete solutions of sweeping processes (i.e. specific first order differential inclusions). The convergence of this numerical scheme was proved thanks to…
This paper studies the Craig variant of the Golub-Kahan bidiagonalization algorithm as an iterative solver for linear systems with saddle point structure. Such symmetric indefinite systems in 2x2 block form arise in many applications, but…
Partial differential equations frequently appear in the natural sciences and related disciplines. Solving them is often challenging, particularly in high dimensions, due to the "curse of dimensionality". In this work, we explore the…
In this paper we give an explicit solution of Dzherbashyan-Caputo-fractional Cauchy problems related to equations with derivatives of order $\nu k$, for $k$ non-negative integer and $\nu>0$. The solution is obtained by connecting the…
Conventional finite-difference schemes for solving partial differential equations are based on approximating derivatives by finite-differences. In this work, an alternative theory is proposed which view finite-difference schemes as…
The linear ordering problem (LOP), which consists in ordering M objects from their pairwise comparisons, is commonly applied in many areas of research. While efforts have been made to devise efficient LOP algorithms, verification of whether…
The performance of the code generated by a compiler depends on the order in which the optimization passes are applied. In high-level synthesis, the quality of the generated circuit relates directly to the code generated by the front-end…
We present a unified framework for designing and analyzing algorithms for online budgeted allocation problems (including online matching) and their generalization, the Online Generalized Assignment Problem (OnGAP). These problems have been…
We introduce efficient differentially private (DP) algorithms for several linear algebraic tasks, including solving linear equalities over arbitrary fields, linear inequalities over the reals, and computing affine spans and convex hulls. As…
We exhibit an online algorithm finding all distinct palindromes inside a given string in time $\Theta(n\log|\Sigma|)$ over an ordered alphabet and in time $\Theta(n|\Sigma|)$ over an unordered alphabet. Using a reduction from a…
In this paper, we give a detailed account of the algorithm outlined in [1] for Feynman integral reduction and $\varepsilon$-factorised differential equations. The algorithm consists of two steps. In the first step, we use a new geometric…
We describe a RAM algorithm computing all runs (maximal repetitions) of a given string of length $n$ over a general ordered alphabet in $O(n\log^{\frac{2}3} n)$ time and linear space. Our algorithm outperforms all known solutions working in…
We transform join ordering into a mixed integer linear program (MILP). This allows to address query optimization by mature MILP solver implementations that have evolved over decades and steadily improved their performance. They offer…
In the Multi-Level Aggregation Problem (MLAP), requests arrive at the nodes of an edge-weighted tree T, and have to be served eventually. A service is defined as a subtree X of T that contains its root. This subtree X serves all requests…
A consequent approach is proposed to construct symplectic force-gradient algorithms of arbitrarily high orders in the time step for precise integration of motion in classical and quantum mechanics simulations. Within this approach the basic…
We investigate the singular sets of solutions of conformally covariant elliptic operators of fractional order with the goal of developing generalizations of some well-known properties of solutions of the singular Yamabe problem.
In this paper, we consider a class of structured nonconvex nonsmooth optimization problems whose objective function is the sum of three nonconvex functions, one of which is expressed in a difference-of-convex (DC) form. This problem class…
Nonlinear elliptic problems arise in many fields, including plasma physics, astrophysics, and optimal transport. In this article, we propose a novel operator-splitting/finite element method for solving such problems. We begin by introducing…