Abstract
This paper describes a restarted Lanczos algorithm that particularly suitable for implementation on distributed machines. The only communication operation is requires outside of the matrix-vector multiplication is a global sum. For most large eigenvalue problems, the global sum operation takes a small fraction of the total execution time. The majority of the computer is spent in the matrix-vector multiplication. Efficient parallel matrix-vector multiplication routines can be found in many parallel sparse matrix packages such as AZTEC [9], BLOCK-SOLVE [10], PETSc [3], P_SPARSLIB. For this reason, our main emphasis in this paper is to demonstrate the correctness and the effectiveness of the new algorithm.
This work was supported by the Director, Office of Energy Research, Office of Laboratory Policy and Infrastructure Management, of the U.S. Department of Energy under Contract No. DE-AC03-76SF00098.
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Wu, K., Simon, H.D. (1998). Thick-restart Lanczos method for symmetric eigenvalue problems. In: Ferreira, A., Rolim, J., Simon, H., Teng, SH. (eds) Solving Irregularly Structured Problems in Parallel. IRREGULAR 1998. Lecture Notes in Computer Science, vol 1457. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0018526
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DOI: https://doi.org/10.1007/BFb0018526
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