Abstract
A three-dimensional mesh implementation of Csanky’s method is shown to be asymptotically faster than systolic algorithms for n × n full matrix inversion. This requires the fastest known sequential matrix multiplication algorithms with large hidden constants. It nevertheless suggests the possibility of o(n) matrix inversion on a scalable architecture with realistic communication costs. Three-dimensional fan-in requirements imply a lower bound of Ω(n ½) or Ω(n 2/3) depending on the input’s spatial distribution. The example of inversion illustrates general methods for optimal mesh implementation of matrix algorithms.
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© 1991 Springer Science+Business Media New York
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Hains, G. (1991). Matrix Inversion in 3 Dimensions. In: Mullin, L.M.R., Jenkins, M., Hains, G., Bernecky, R., Gao, G. (eds) Arrays, Functional Languages, and Parallel Systems. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4002-1_16
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DOI: https://doi.org/10.1007/978-1-4615-4002-1_16
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