We present a Ritz-Galerkin discretization on sparse grids using pre-wavelets, which allows to solve elliptic differential equations with variable coefficients for dimension d = 2, 3 and higher dimensions d > 3. The method applies multilinear finite elements. We introduce an efficient algorithm for matrix vector multiplication using a Ritz-Galerkin discretization and semi-orthogonality. This alg...

It is a well-known fact that while reducing a symmetric matrix into a similar tridiagonal one, the already tridiagonal matrix in the partially reduced matrix has as eigenvalues the Lanczos-Ritz values (see e.g. [Golub G. and Van Loan C.] ). This behavior is also shared by the reduction algorithm which transforms symmetric matrices via orthogonal similarity transformations to semiseparable form ...

The impact of emergency nursing roles in demand management systems is poorly understood. The aim of this study was to evaluate emergency nurses' role in a specific emergency department (ED) demand management system: rapid intervention and treatment zone (RITZ). A descriptive exploratory approach was used. Data were collected from audit of 193 randomly selected patient records and 12 h of clinic...

Preconditioned gradient iterations for very large eigenvalue problems are efficient solvers with growing popularity. However, only for the simplest preconditioned eigensolver, namely the preconditioned gradient iteration (or preconditioned inverse iteration) with fixed step size, sharp non-asymptotic convergence estimates are known. These estimates require a properly scaled preconditioner. In t...

The Rydberg formula along with the Ritz quantum defect ansatz has been a standard theoretical tool used in atomic physics since before advent of mechanics, yet this approach remained limited by its nonrelativistic foundation. Here I present long-distance relativistic effective theory describing hydrogenlike systems arbitrary mass ratios, thereby extending canonical Ritz-like approach. Fitting t...