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Given N matrices A_{1}, A_{2},…, A_{N } of size N×N, the matrix chain product problem is to compute A_{1}×A_{2}×···A_{N }. Given an N×N matrix A, the matrix powers problem is to calculate the first N powers of A, i.e., A, A^{2}A^{3},…, A^{N}. We consider distributed memory systems (DMS) with p processors that can support one-to-one communications in O(T(p)) time. Assume that the time complexity of the best known sequential algorithm for matrix multiplication is O(N^{α}), where α<2.3755. Let p be arbitrarily chosen in the range 1⩽p⩽N^{α+1}/log N. We show that the two problems can be solved on a p-processor DMS in T _{chain}(N,p)=O(N^{α+1}/p+T(p)(N ^{2(1+1/α)}/p^{2}/ ^{α}(log p/N)^{1-2}α/+log(p log N/N^{α}) log N)) and T_{power}(N,p)=0(N^{α+1}/p+T(p)(N ^{2(1+1/α)}/p^{2}/ ^{α}(log p/log N) ^{1-2}α/+(log N)^{2})) times, respectively. We also give instantiation of the above results in distributed memory parallel computers and DMS with hypercubic networks, and show that our parallel algorithms are either fully scalable or highly scalable

- Meeting Date :
- 23 Apr 2001-27 Apr 2001
- ISSN :
- 1530-2075
- Print ISBN:
- 0-7695-0990-8
- INSPEC Accession Number:
- 6964417

- Conference Location :
- San Francisco, CA
- DOI:
- 10.1109/IPDPS.2001.924937
- Publisher:
- IEEE