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The concept of pseudospectrum was introduced by L. N. Trefethen to explain the behavior of nonnormal operators. Many phenomena (for example, hydrodynamic instability and convergence of iterative methods for linear systems) cannot be accounted for by eigenvalue analysis but are more understandable by examining the pseudospectra. The straightforward way to… (More)

The Schwarz Alternating Method can be used to solve elliptic boundary value problems on domains which consist of two or more overlapping subdomains. The solution is approximated by an innnite sequence of functions which results from solving a sequence of elliptic boundary value problems in each of the subdomains. This paper considers several Schwarz… (More)

The Schwarz alternating method can be used to solve linear elliptic boundary value problems on domains which consist of two or more overlapping subdomains. The solution is approximated by an innnite sequence of functions which result from solving a sequence of elliptic boundary value problems in each of the subdomains. This paper considers four Schwarz… (More)

The Schwarz Alternating Method can be used to solve elliptic boundary value problems on domains which consist of two or more overlapping subdomains. The solution is approximated by an innnite sequence of functions which results from solving a sequence of elliptic boundary value problems in each of the subdomains. In this paper, proofs of convergence of some… (More)