Factorization Of Positive Definite, Banded Hermitian Matrices

Report discusses application of Cholesky factorization algorithm to positive definite, banded Hermitian matrices. Begins by extending Cholesky factorization algorithm to cover uniformly-partitioned, banded, positive definite matrices of rank n that is real symmetric or Hermitian. Then two stratagems given for use of algorithm in concurrent-processing system in which N less than it has to be to enable factorization of matrix in as few serial steps as possible and where uniformly high efficiency expected from all processing elements. One of major purposes of this and related studies to maximize speedup and efficiency in system of concurrent-data-processing elements.