Abstract
The Lanczos method has been conventionally utilized as an eigenvalue solver for huge size matrices encountered in strongly correlated fermion systems. However, since one can not obtain the residual during the Lanczos iteration, the iteration count in the Lanczos method is not controllable. Thus, we adopt a new eigenvalue solver based on the conjugate gradient (CG) method in which the residual can be evaluated every iteration step. We confirm that the CG method with an preconditioner shows much more excellent performance than the Lanczos method. We achieve 16.14 TFLOPS on 512 nodes (4096 processors) of the Earth Simulator by the use of the CG method.
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Yamada, S., Imamura, T., Machida, M. (2008). 16.14 TFLOPS Eigenvalue Solver on the Earth Simulator: Exact Diagonalization for Ultra Largescale Hamiltonian Matrix. In: Labarta, J., Joe, K., Sato, T. (eds) High-Performance Computing. ISHPC ALPS 2005 2006. Lecture Notes in Computer Science, vol 4759. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77704-5_38
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DOI: https://doi.org/10.1007/978-3-540-77704-5_38
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