Submitted to the proceedings of the ninth international conference on domain decomposition methods (Bergen-Norway-1996).

We show that the decreasing dimension method proposed by Wang and Jiang in \Solution of the System of Linear Algebraic Equations by Decreasing Dimension", Appl. Math. Comput, 109 (2000) 51{57, is a type of Schur complement domain decomposition method. The decreasing dimension method is more expensive than the standard Schur complement domain decomposition method for solving any linear systems. ...

This paper presents a parallel mixed direct/iterative method for solving linear systems Ax = b arising from circuit simulation. The systems are solved by a block LU factorization with an iterative method for the Schur complement. The Schur complement is a small and rather dense matrix. Direct LU decomposition of the Schur complement takes too much time in order to achieve reasonable speedup res...

We show how to cheaply estimate the Fr echet derivative and the condition number for a general class of matrix functions (the class includes the matrix sign function and functions that can be expressed as power series) via the Schur decomposition. In the case of the matrix sign function we also give a method to compute the Fr echet derivative exactly. We also show that often this general method...

AbRtract This paper deals with the domain decomposition-based preconditioned conjugate gradient method. The Schur complement is expressed as a function of & simple interface matrix. This function is approximated by a simple rational function to generate a simple matrix that is then used 8.8 & preconditioner for the Schur complement. Extensive experiments are performed to examine the effectivene...

Interface boundary conditions are the key ingredient to design efficient domain decomposition methods. However, convergence cannot be obtained for any method in a number of iterations less than the number of subdomains minus one in the case of a one-way splitting. This optimal convergence can be obtained with generalized Robin type boundary conditions associated with an operator equal to the Sc...

To rely on authenticity of Image we can use Image Watermarking. In this Paper a new robust Image watermarking algorithm is proposed, which is based on Schur decomposition. Schur decomposition gives good result in terms of performance, robustness, imperceptibility and speed etc Schur decomposition technique shows a good performance against the various attacks such as JPEG compression, cropping, ...

The aim of this paper is to give a unified comparison of non-overlapping domain decomposition methods (DDMs) for solving magnetic field problems. The methods under investigation are the Schur complement method and the Lagrange multiplier based Finite Element Tearing and Interconnecting (FETI) method, and their solvers. The performance of these methods has been investigated in detail for two-dim...

Domain decomposition algorithms have received much attention in the last decade [2]. The domain in which a differential equation is defined is partitioned in several subdomains, and the equation is solved in these domains. The local results are integrated to form the solution in the entire domain. Since the subdomains can be solved in parallel, domain decomposition has become very popular on pa...