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|Title:||FAST PARALLEL BAND MATRIX ARITHMETIC|
|Abstract:||We present parallel algorithms for computation of the determinant, adjoint, characteristic polynomial and rank of band matrices, and for the solution of systems of linear equations with band matrices as coefficient matrices. The algorithms can be implemented using arithmetic-boolean circuits of polynomial size and depth O(log n logm), or depth O(log n log m + log n log log n) for computations over small finite fields, where n is the order and m the band width of the matrix given as input. They can be implemented for computations over number fields and finite fields using log space uniform boolean circuits of depth O(log n log m + log n log log n) and polynomial size, for input size n and band width m.|
|Appears in Collections:||Eberly, Wayne|
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