Parallel Algorithms

Parallel Cholesky Factorization of a SPD Matrix with MPI

In this paper we present parallel Cholesky factorization. This method is widely used for numerical solutions inter alia of linear equations. Realization of decomposition will be done with a use of the Message Passing Interface (MPI). The Cholesky decomposition (or Cholesky factorization) is a decomposition of a Hermitian (complex-valued matrix that coincides with its own conjugate transpose) and positive-definite into the product of a lower triangular matrix and its conjugate transpose (it can be considered as a special case of the more general LU decomposition). An LU decomposition is a factorization of a matrix into a lower triangular matrix L, an upper triangular matrix U, and a permutation matrix P, used in numerical analysis to solve a system of linear equations, to calculate the inverse of a matrix or to calculate the determinant of a matrix.