We present an algorithm for the solution of a simultaneous space-time discretization linear parabolic evolution equations with symmetric differential operator in space. Building on earlier work, we recast this into Schur-complement equation whose is quasi-optimal approximation to weak at hand. Choosing tensor-product discretization, arrive remarkably simple system. Using wavelets time and stand...

Edge-oriented stabilization methods in the framework of discontinuous Galerkin approaches have been recently proposed by Brenner [3] and particularly by Hansbo and Larson [5] for nonconforming finite element discretizations to satisfy a discrete Korn’s inequality. We develop and analyse corresponding multigrid components in combination with local Pressure-Schur-Complement methods and give numer...

Two method for computation of the spectra certain infinite graphs are suggested. The first one can be viewed as a reversed Gram--Schmidt orthogonalization procedure. It relies heavily on spectral theory Jacobi matrices. second is related to Schur complement block A number examples including with tails, chains cycles and ladders worked out in detail.

Cyclic reduction was conceived for the solution of tridiagonal linear systems, such as the one-dimensional Poisson equation [11]. Generalized to higher dimensions, it is known as block cyclic reduction (BCR) [4]. It can be used for general (block) Toeplitz and (block) tridiagonal linear systems; however, it is not competitive for large problems, because its arithmetic complexity grows superline...

The generalized inverse has numerous important applications in aspects of the theoretic research matrices and statistics. One core problems is finding necessary sufficient conditions for reverse (or forward) order laws matrix products. In this paper, by using extremal ranks Schur complement, some are given forward law A1{1,2}A2{1,2}…An{1,2}⊆(A1A2…An){1,2}.

A new class of high-performance preconditioned iterative solution methods for large-scale finite element method (FEM) elliptic systems is proposed and analyzed. The non-overlapping domain decomposition (DD) naturally introduces coupling operator at the interface γ. In general, γ a manifold lower dimensions. At level, key property that energy norm associated with Steklov-Poincaré spectrally equi...