Implementation and parallelization of fast matrix multiplication for a fast Legendre transform
- Denison Univ., Granville, OH (United States)
An algorithm was presented by Alpert and Rokhlin for the rapid evaluation of Legendre transforms. The fast algorithm can be expressed as a matrix-vector product followed by a fast cosine transform. Using the Chebyshev expansion to approximate the entries of the matrix and exchanging the order of summations reduces the time complexity of computation from O(n{sup 2}) to O(n log n), where n is the size of the input vector. Our work has been focused on the implementation and the parallelization of the fast algorithm of matrix-vector product. Results have shown the expected performance of the algorithm. Precision problems which arise as n becomes large can be resolved by doubling the precision of the calculation.
- Research Organization:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Sponsoring Organization:
- USDOE, Washington, DC (United States); Great Lakes Colleges Association/Associated Colleges of the Midwest (United States)
- DOE Contract Number:
- AC05-84OR21400
- OSTI ID:
- 10192072
- Report Number(s):
- ORNL/TM-12285; ON: DE94002184
- Resource Relation:
- Other Information: PBD: Sep 1993
- Country of Publication:
- United States
- Language:
- English
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