The algebraic eigenvalue problem
The algebraic eigenvalue problem
Solving narrow banded systems on ensemble architectures
ACM Transactions on Mathematical Software (TOMS)
Computer Solution of Large Sparse Positive Definite
Computer Solution of Large Sparse Positive Definite
| Hi-index | 14.98 |
The inherent strong seriality of closely coupled systems is circumvented by defining a family of permutations for reordering equation sets whose matrix of coefficients is Hermitian block tridiagonal. The authors show how these permutations can be used to achieve relatively high concurrency in the Cholesky factorization of banded systems at the expense of introducing limited extra computations due to fill-in terms in the factors. Directed graphs are developed for the concurrent factorization of the transformed matrix of coefficients by the Cholesky algorithm. Expressions for speedup and efficiency are derived in terms of parameters of the permutation, set of equations, and machine architecture.