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Inner Products.

The computation of an inner product of two vectors can be easily parallelized; each processor computes the inner product of corresponding segments of each vector (local inner products (LIPs)). On distributed memory machines the LIPs then have to be sent to other processors to be combined for the global inner product. This can be done either with an all-to-all send where every processor performs the summation of the LIPs, or by a global accumulation in one processor, followed by a broadcast of the final result. Clearly, this step requires communication.

For shared memory machines, the accumulation of LIPs can be implemented as a critical section where all processors add their local result in turn to the global result, or as a piece of serial code, where one processor performs the summations.

Susan Blackford 2000-11-20