Preconditioning by Fast Direct Methods for Non-Self-Adjoint Nonseparable Elliptic Equations.
YALE UNIV NEW HAVEN CT DEPT OF COMPUTER SCIENCE
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We consider the use of fast direct methods as preconditioners for iterative methods for computing the numerical solution of non-self-adjoint elliptic boundary value problems. We derive bounds on convergence rates that are independent of discretization mesh size. For two-dimensional problems on rectangular domains, discretized on an nxn grid, these bounds lead to asymptotic operation counts of On squared log n 1log epsilon to achieve relative error epsilon and On squared log n squared to reach truncation error.
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