osting by E Abstract In this paper, we consider and analyze some classes of resolvent-splitting methods for solving the general variational inclusions using the technique of updating the solution. These resolvent-splitting methods are self-adaptive-type methods, where the corrector step size involves the resolvent equation. We prove that the convergence of these new methods only require the pse...

This work presents an alternative formulation of resolvent analysis based on the calculus variations. The proposed circumvents reliance inversion linear operator and is inherently compatible with any arbitrary choice norm. Several examples are presented which highlight analytical numerical advantages limitations formulation.

One of the conditions in the Kreiss matrix theorem involves the resolvent of the matrices A under consideration. This so-called resolvent condition is known to imply, for all n ≥ 1, the upper bounds ‖An‖ ≤ eK(N + 1) and ‖An‖ ≤ eK(n + 1). Here ‖ · ‖ is the spectral norm, K is the constant occurring in the resolvent condition, and the order of A is equal to N + 1 ≥ 1. It is a long-standing proble...

In recent years several papers have been devoted to stability and smoothing properties in maximum-norm of finite element discretizations of parabolic problems. Using the theory of analytic semigroups it has been possible to rephrase such properties as bounds for the resolvent of the associated discrete elliptic operator. In all these cases the triangulations of the spatial domain has been assum...

This paper is devoted to a sharp investigation of the notion of Lagrange's resolvent and his connections with Galois Theory.

The link between modular functions and algebraic was a driving force behind the 19th century study of both. Examples include solutions by Hermite Klein quintic via elliptic general sextic level 2 hyperelliptic functions. This paper aims to apply modern arithmetic techniques circle “resolvent problems” formulated pursued Klein, Hilbert others. As one example, we prove that essential dimension at...