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- W1984965528 abstract "Bordered almost block diagonal systems arise from discretizing a linearized first-order system of n ordinary differential equations in a two-point boundary value problem with nonseparated boundary conditions. The discretization may use spline collocation, finite differences, or multiple shooting. After internal condensation, if necessary, the bordered almost block diagonal system reduces to a standard finite difference structure, which can be solved using a preconditioned conjugate gradient method based on a simple matrix splitting technique. This preconditioned conjugate gradient method is “guaranteed” to converge in at most 2 n + 1 iterations. We exhibit a significant collection of two-point boundary value problems for which this preconditioned conjugate gradient method is unstable, and hence, convergence is not achieved." @default.
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- W1984965528 date "1995-12-01" @default.
- W1984965528 modified "2023-09-27" @default.
- W1984965528 title "Convergence and instability in PCG methods for bordered systems" @default.
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- W1984965528 doi "https://doi.org/10.1016/0898-1221(95)00177-z" @default.
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