抄録
Offer Organization: Japan Society for the Promotion of Science, System Name: Grants-in-Aid for Scientific Research, Category: Grant-in-Aid for Challenging Research (Exploratory), Fund Type: -, Overall Grant Amount: - (direct: 4700000, indirect: 1410000)
The aim of this study is to develop new algorithms for matrix computations based on non-orthogonal transformations and analyze their convergence properties and accuracy theoretically. We chose the time-dependent eigenvalue problem and preconditioning methods for iterative solution of linear systems as examples. For the former, we developed an algorithm based on matrix multiplications, which is suited for next-generation microprocessors. For the latter, we developed a highly parallel algorithm based on the modified incomplete Cholesky factorization and the block red-block ordering.