In the framework of abstract linear inverse problems in infinite-dimensional Hilbert space we discuss generic convergence behaviours approximate solutions determined by means general projection methods, namely outside standard assumptions Petrov–Galerkin truncation schemes. This includes a discussion mechanisms why error or residual generically fail to vanish norm, and identification practicall...

Large-scale dynamical networks (dynamical systems on large-scale complex networks), whose behaviors are described by the interaction of a large number of subsystems, have been extensively studied over the past decades. Examples of such dynamical networks include biological networks, power networks, traffic networks; see [1, 2] for an overview. In order to control large-scale systems, the model ...

Projector-based embedding is a relatively recent addition to the collection of methods that seek utilize chemical locality provide improved computational efficiency. This work considers interactions between different proposed procedures for this method and their effects on accuracy results. The interplay embedded background, projector type, partitioning scheme, level atomic orbital (AO) truncat...

This paper presents a study of the behavior of several difference approximations for the incompressible Navier–Stokes equations as a function of the computational mesh resolution. In particular, the under-resolved case is considered. The methods considered include a Godunov projection method, a primitive variable ENO method, an upwind vorticity stream-function method, centered difference method...

The pseudofermion representation for $S=1/2$ quantum spins introduces unphysical states in the Hilbert space, which can be projected out using Popov-Fedotov trick. However, state-of-the-art implementation of functional renormalization group method pseudofermions have so far omitted projection. Instead, restrictions to zero temperature were made and absence contributions ground state was assumed...

This paper presents a study of the behavior of several di erence approximations for the incompressible Navier-Stokes equations as a function of the computational mesh resolution. In particular, the under-resolved case is considered. The methods considered include a Godunov projection method, a primitive variable ENO method, an upwind vorticity stream-function method, centered di erence methods ...

The purpose of this study was to improve the speed of the Simultaneous Algebraic Reconstruction Technique (SART) for truncated cone-beam (CB) projections using a distance-driven forward projector. First, we optimized the innermost loop of the projector for a cone-beam scanner with a circular source trajectory and a flat-panel imager. We showed that the innermost loop of the distance-driven proj...

In this paper we propose a state estimation method for linear parabolic partial differential equations (PDE) that accounts for errors in the model, truncation, and observations. It is based on an extension of the Galerkin projection method. The extended method models projection coefficients, representing the state of the PDE in some basis, by means of a differential-algebraic equation (DAE). Th...

Compared with complex and lengthy Gauss-Krüger projection series expansions real number expressions, we improve the function representation of projections rewrite them into “multiple Angle form”, “exponential “double form”. The coefficients were expanded in power based on first eccentricity e third flattening n, respectively, truncation difference was analyzed when to different orders obtain si...

In this paper we consider the numerical solution of projected generalized continuous-time Lyapunov equations with low-rank right-hand sides. The interest in this problem stems from stability analysis and control problems for descriptor systems including model reduction based on balanced truncation. Two projection methods are proposed for calculating low-rank approximate solutions. One is based ...