Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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. >
['Senol Utku', 'Moktar Salama', 'R. J. Melosh']
I am writing a research paper on a idea A family of permutations for concurrent factorization of block tridiagonal matrices
[{"from": "human", "value": "I am writing a research paper on a idea A family of permutations for concurrent factorization of block tridiagonal matrices"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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. >"}]