Basic HTML version of Foils prepared August 7 98

Foil 22 Conjugate Gradient: Partitioning

From DoD HPF Training -- 5. Parallel Programming in HPF DoD Training and Others -- 1995-98. by Chuck Koelbel -- Rice University


1 At the most abstract level, conjugate gradient has minimal parallelism
  • u, r, a can be updated independently
2 The real potential parallelism is in the matrix and vector operations, however.
  • r × r is a reduction of size N
  • u + a p is a vector update of size N
  • A * p is a (sparse) matrix-vector multiply, in this case of size O(N)
    • It looks a lot like the operator in Jacobi
3 Conclusions:
  • Stick to the matrix/vector operators
  • Task parallelism (and pipelining) may improve some

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