相关论文: On two families of iterative methods without memor…

Discrete gradient methods are a class of numerical integrators producing solutions with exact preservation of first integrals of ordinary differential equations. In this paper, we apply order theory combined with the symmetrized Itoh--Abe…

We study and derive algorithms for nonlinear eigenvalue problems, where the system matrix depends on the eigenvector, or several eigenvectors (or their corresponding invariant subspace). The algorithms are derived from an implicit…

We introduce a new family of meta-Fibonacci sequences $(f(n))_{n\in\mathbb{N}}$, governed by the recurrence relation $$f(n)=af(n-u_{n}-1)+bf(n-u_{n}-2),$$ where $\mathbf{u}=(u_{n})_{n\in \mathbb{N}}$ is a sequence with values $0,1$. Our…

We characterize bivariate natural exponential families having the diagonal of the variance function of the form \[ \textrm{diag} V(m_1,m_2)=\left(Am_1^2+am_1+bm_2+e,Am_2^2+cm_1+dm_2+f\right), \] with $A<0$ and $a,\ldots,f\in\mathbb{R}$. The…

We find a strong separation between two natural families of simple rank one theories in Keisler's order: the theories $T_\mathfrak{m}$ reflecting graph sequences, which witness that Keisler's order has the maximum number of classes, and the…

Many important applications are modelled by differential equations with positive solutions. However, it remains an outstanding open problem to develop numerical methods that are both (i) of a high order of accuracy and (ii) capable of…

We develop a one step matrix method in order to obtain approximate solutions of first order systems and non-linear ordinary differential equations, reducible to first order systems. We find a sequence of such solutions that converge to the…

In a first part, we give a method for solving a family of fuchsian systems of operators of pseudo-derivations associated to a family of homographies with two parameters which unify and generalize the differential, the difference and the…

The main objective of this paper is the following two results. (1) There exists a computable bi-orderable group that does not have a computable bi-ordering; (2) There exists a bi-orderable, two-generated recursively presented solvable group…

We investigate the use of piecewise linear systems, whose coefficient matrix is a piecewise constant function of the solution itself. Such systems arise, for example, from the numerical solution of linear complementarity problems and in the…

In this paper, we analyze a family of hybridizable discontinuous Galerkin (HDG) methods for second order elliptic problems in two and three dimensions. The methods use piecewise polynomials of degree $k\geqslant 0$ for both the flux and…

Group theoretical methods are used to study some properties of the Riccati equation, which is the only differential equation admitting a nonlinear superposition principle. The Wei-Norman method is applied to obtain the associated…

A new method for finding first integrals of discrete equations is presented. It can be used for discrete equations which do not possess a variational (Lagrangian or Hamiltonian) formulation. The method is based on a newly established…

We introduce new optimized first-order methods for smooth unconstrained convex minimization. Drori and Teboulle recently described a numerical method for computing the $N$-iteration optimal step coefficients in a class of first-order…

A matrix factorization problem is considered. The matrix to be factorized is algebraic, has dimension 2 X 2 and belongs to Moiseev's class. A new method of factorization is proposed. First, the matrix factorization problem is reduced to a…

We review some recent developments in numerical algorithms to solve the time-dependent Maxwell equations for systems with spatially varying permittivity and permeability. We show that the Suzuki product-formula approach can be used to…

For relatively prime natural numbers $a$ and $b$, we study the two equations $ax+by = (a-1)(b-1)/2$ and $ax+by+1= (a-1)(b-1)/2$, which arise from the study of cyclotomic polynomials. Previous work showed that exactly one equation has a…

Each family of Gauss hypergeometric functions $$ f_n={}_2F_1(a+\epsilon_1n, b+\epsilon_2n ;c+\epsilon_3n; z), $$ for fixed $\epsilon_j=0,\pm1$ (not all $\epsilon_j$ equal to zero) satisfies a second order linear difference equation of the…

Many machine learning models depend on solving a large scale optimization problem. Recently, sub-sampled Newton methods have emerged to attract much attention for optimization due to their efficiency at each iteration, rectified a weakness…

Variational inequalities represent a broad class of problems, including minimization and min-max problems, commonly found in machine learning. Existing second-order and high-order methods for variational inequalities require precise…