We give a solution to the inverse moment problem for a certain class of Hessenberg and symmetric matrices related to integrable lattices of Toda type.

This work proposes a new adaptive remeshing strategy based on the sensitivity of the point wise error in stresses with respect to the nodal coordinates, which is computed using the adjoint-state method. This sensitivity provides information about the influence of the discretization of each zone of the computational domain in the estimation of the error in stresses at a specific point. This info...

Adaptivity in both space and time has become the norm for solving problems modeled by partial differential equations. The size of the discretized problem makes uniformly refined grids computationally prohibitive. Adaptive refinement of meshes and time steps allows to capture the phenomena of interest while keeping the cost of a simulation tractable on the current hardware. Many fields in scienc...

The importance of good estimates of the defect in the numerical solution of initial value problem ordinary differential equations is considered in the context of global error estimation by using adjoint-equation based methods. In the case of solvers based on the fixed leading coefficient backward differentiation formulae, the quality of defect estimates is shown to play a major role in the reli...

A wavelet regularization approach is presented for dealing with an ill-posed problem of adjoint parameter estimation applied to estimating inflow parameters from down-flow data

Abstract We develop a categorical index calculus for elliptic symbol families. The categorified problems we consider are secondary version of the traditional problem expressing class in K-theory terms differential-topological data. They include orientation moduli spaces as well similar skew-adjoint and self-adjoint operators. main result this paper is an excision principle that allows compariso...

The objective of this article is to formalize the definition of NP problems. We construct a mathematical model of discrete problems as independence systems with weighted elements. We introduce two auxiliary sets that characterize the solution of the problem: the adjoint set, which contains the elements from the original set none of which can be adjoined to the already chosen solution elements; ...