Related papers: Local approximation of the solutions of algebraic …
This paper presents a method for computing eigenvalues and eigenvectors for some types of nonlinear eigenvalue problems. The main idea is to approximate the functions involved in the eigenvalue problem by rational functions and then apply a…
We describe, up to isomorphism, all locally simple subalgebras of any diagonal locally simple Lie algebra.
This work proposes a discretization of the acoustic wave equation with possibly oscillatory coefficients based on a superposition of discrete solutions to spatially localized subproblems computed with an implicit time discretization. Based…
A numerical method to solve linear integro-differential equations is presented. This method has been used to solve the QCD Altarelli-Parisi evolution equations within the H1 Collaboration at DESY-Hamburg. Mathematical aspects and numerical…
Real algebraic geometry adapts the methods and ideas from (complex) algebraic geometry to study the real solutions to systems of polynomial equations and polynomial inequalities. As it is the real solutions to such systems modeling…
We study local regularity properties for solutions of linear, non-uniformly elliptic equations. Assuming certain integrability conditions on the coefficient field, we prove local boundedness and Harnack inequality. The assumed integrability…
The moving coframe method is applied to solve the local equivalence problem for the class of linear parabolic equations in two independent variables under an action of the pseudo-group of contact transformations. The structure equations and…
We study the numerical simulation of supersymmetric models having a local Nicolai map. The mapping can be regarded as a stochastic equation and its numerical integration provides an algorithm for the simulation of the original model. In…
A novel method, connecting the space of solutions of a linear differential equation, of arbitrary order, to the space of monomials, is used for exploring the algebraic structure of the solution space. Apart from yielding new expressions for…
We establish an effective improvement on the Liouville inequality for approximation to complex non-real algebraic numbers by quadratic complex algebraic numbers.
We study the optimal approximation of the solution of an operator equation Au=f by linear and nonlinear mappings.
In this work, an efficient approximation scheme has been proposed for getting accurate approximate solution of nonlinear partial differential equations with constant or variable coefficients satisfying initial conditions in a series of…
We construct standard resolutions for analytic local modules on complex hypersurfaces using standard basis methods, with extensions to complete intersections. The algebraic version over arbitrary infinite fields is also suggested.…
We first propose two conjectural estimates on Diophantine approximation of logarithms of algebraic numbers. Next we discuss the state of the art and we give further partial results on this topic.
In this paper we present algorithms that compute certain local cohomology modules associated to a ring of polynomials containing the rational numbers. In particular we are able to compute the local cohomological dimension of algebraic…
Algebraic effects are computational effects that can be described with a set of basic operations and equations between them. As many interesting effect handlers do not respect these equations, most approaches assume a trivial theory,…
The numerical methods for differential equation solution allow obtaining a discrete field that converges towards the solution if the method is applied to the correct problem. Nevertheless, the numerical methods have the restricted class of…
Numerical homogenization methods aim at providing appropriate coarse-scale approximations of solutions to (elliptic) partial differential equations that involve highly oscillatory coefficients. The localized orthogonal decomposition (LOD)…
We consider finite element methods of multiscale type to approximate solutions for two-dimensional symmetric elliptic partial differential equations with heterogeneous $L^\infty$ coefficients. The methods are of Galerkin type and follow the…
In this article we provide examples, methods and algorithms to determine conditions on the parameters of certain type of parametric optimization problems, such that among the resulting local minima and maxima there is at least one which…