Generalized scans and tri-diagonal systems
The classical problem of solving tridiagonal linear systems of equations is reconsidered. An extremely simple factorization of the system's matrix — implied by but not explicit in the known techniques — is identified and shown to belong to a class of transformations termed generalized scans. This class has an associative property which is the key to the complete parallelization of the technique. Due to the very weak constraints upon which it is based, the method extends naturally to arbitrary banded systems.
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