Parallel solution of large symmetric tridiagonal linear systems
Parallel Computing
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The solution of linear, tridiagonal systems having real, symmetric, diagonally dominant coefficient matrices with constant diagonals is considered. Details of cyclic reduction to solve such systems are discussed. It is proved that the sequence of the diagonal elements produced by the reduction phase of cyclic reduction converges quadratically. This fact is exploited to reduce the number of steps of the reduction phase (special cyclic reduction). An estimate of the rate of convergence of the diagonal elements will be proved, which can be used to determine the number of steps of the reduction phase. Several possibilities to compute the diagonal elements are discussed and compared.