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An equation containing a fractional power of an elliptic operator of second order is studied for Dirichlet boundary conditions. Finite difference approximations in space are employed. The proposed numerical algorithm is based on solving an…
We study the problem of scheduling a general computational DAG on multiple processors in a 2-level memory hierarchy. This setting is a natural generalization of several prominent models in the literature, and it simultaneously captures…
We present an algorithm for determining the minimal order differential equations associated to a given Feynman integral in dimensional or analytic regularisation. The algorithm is an extension of the Griffiths-Dwork pole reduction adapted…
A class of splitting alternating algorithms is proposed for finding the sparse solution of linear systems with concatenated orthogonal matrices. Depending on the number of matrices concatenated, the proposed algorithms are classified into…
We derive an efficient algorithm to find solutions to Euler's concordant form problem and rational points on elliptic curves associated with this problem.
Floor planning is an important and difficult task in architecture. When planning office buildings, rooms that belong to the same organisational unit should be placed close to each other. This leads to the following NP-hard mathematical…
Let $G$ be a finite solvable group, given through a refined consistent polycyclic presentation, and $\alpha$ an automorphism of $G$, given through its images of the generators of $G$. In this paper, we discuss algorithms for computing the…
Much algorithmic research in NLP aims to efficiently manipulate rich formal structures. An algorithm designer typically seeks to provide guarantees about their proposed algorithm -- for example, that its running time or space complexity is…
The problem of detecting of information and logically independent (DILD) steps in programs is a key for equivalent program transformations. Here we are considering the problem of independence of loop iterations, the concentration of massive…
The purpose of this paper is to propose a semi-analytical technique convenient for numerical approximation of solutions of the initial value problem for $p$-dimensional delayed and neutral differential systems with constant, proportional…
We describe a class of the singular solutions to the multicomponent analogs of the Lam{\'e} equation, arising as equations of motion of the elliptic Calogero--Moser systems of particles carrying spin 1/2. At special value of the coupling…
We present a new certified and complete algorithm to compute arrangements of real planar algebraic curves. Our algorithm provides a geometric-topological analysis of the decomposition of the plane induced by a finite number of algebraic…
We present a family of fast and accurate Dijkstra-like solvers for the eikonal equation and factored eikonal equation which compute solutions on a regular grid by solving local variational minimization problems. Our methods converge…
We describe an algorithm for the numerical solution of second order linear differential equations in the highly-oscillatory regime. It is founded on the recent observation that the solutions of equations of this type can be accurately…
Planning in hybrid systems with both discrete and continuous control variables is important for dealing with real-world applications such as extra-planetary exploration and multi-vehicle transportation systems. Meanwhile, generating…
This paper shows how to build a formal analytical solution for a differential equation of arbitrary order and with variable coefficients. It proofs that the most known approximated solutions for such a problem can be derived from the…
We have been working in many aspects of the problem of analyzing, understanding and solving ordinary differential equations (first and second order). As we have extensively mentioned, while working in the Darboux type methods, the most…
A conforming discontinuous Galerkin finite element method is introduced for solving the biharmonic equation. This method, by its name, uses discontinuous approximations and keeps simple formulation of the conforming finite element method at…
We present a generalization of the $x$-space $\texttt{Candia}$ algorithm to next-to-next-to-next-to-leading order (N$^3$LO) accuracy in Quantum Chromodynamics (QCD) for solving the DGLAP evolution equations for unpolarized parton densities…
We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the $H^{-1}$-gradient flow of the…