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This paper is about GMRES algorithms for the solution of nonsingular linear systems. We first consider basic algorithms and study their convergence. We then focus on acceleration strategies and parallel algorithms that are useful for…
We classify hyperbolic polynomials in two real variables that admit a transitive action on some component of their hyperbolic level sets. Such surfaces are called special homogeneous surfaces, and they are equipped with a natural Riemannian…
We give several algorithms addressing computations of intersections of conjugate subgroups.
In this article we determine several theorems and methods for solving linear congruences and systems of linear congruences, and we find the number of distinct solutions. Many examples of solving congruences are given.
This paper is concerned with homogenization of systems of linear elasticity with rapidly oscillating periodic coefficients. We establish sharp convergence rates in $L^2$ for the mixed boundary value problems with bounded measurable…
In this paper we presents an algorithm for finding a solution of the linear nonhomogeneous quaternionic-valued differential equations. Moveover, several examples shows the feasibility of our algorithm.
We consider the problem of solving a large-scale system of linear equations in a distributed or federated manner by a taskmaster and a set of machines, each possessing a subset of the equations. We provide a comprehensive comparison of two…
Some methods based on simple regularizing geometric element transformations have heuristically been shown to give runtime efficient and quality effective smoothing algorithms for meshes. We describe the mathematical framework and a…
A simple and efficient algorithm to numerically compute the genus of surfaces of three-dimensional objects using the Euler characteristic formula is presented. The algorithm applies to objects obtained by thresholding a scalar field in a…
We use orbifold structures to deduce degeneracy statements for holomorphic maps into logarithmic surfaces. We improve former results in the smooth case and generalize them to singular pairs. In particular, we give applications on nodal…
In this paper we provide, first, a general symbolic algorithm for computing the symmetries of a given rational surface, based on the classical differential invariants of surfaces, i.e. Gauss curvature and mean curvature. In practice, the…
The goal of this paper is to exhibit and analyze an algorithm that takes a given closed orientable hyperbolic surface and outputs an explicit Dirichlet domain. The input is a fundamental polygon with side pairings. While grounded in…
In this article, we discuss formal invariants of singularly-perturbed linear differential systems in neighborhood of turning points and give algorithms which allow their computation. The algorithms proposed are implemented in the computer…
This survey focuses on the computational complexity of some of the fundamental decision problems in 3-manifold theory. The article discusses the wide variety of tools that are used to tackle these problems, including normal and almost…
We consider linear problems in the worst case setting. That is, given a linear operator and a pool of admissible linear measurements, we want to approximate the values of the operator uniformly on a convex and balanced set by means of…
We consider the solution of initial value problems within the context of hybrid systems and emphasise the use of high precision approximations (in software for exact real arithmetic). We propose a novel algorithm for the computation of…
Let $S$ be a smooth projective surface with $p_g=q=0$. We show how to use derived categorical methods to study the geometry of certain special iterated Hilbert schemes associated to $S$ by showing that they contain a smooth connected…
Subject of this paper is an implementation of a well-known Motzkin-Burger algorithm, which solves the problem of finding the full set of solutions of a system of linear homogeneous inequalities. There exist a number of implementations of…
In a previous work of the authors, a result to algorithmically compute the topology types of the level curves of an algebraic surface, is given. From this result, here we derive applications based on level curves to determine some…
In this note we relate about the problem of evaluate the dimension of linear systems through fat points defined on generic $K3$ surfaces.