Matrix-vector communication, parallel

Outline of a simple parallel algorithm to perform the matrix-vector multiplication Ab = c. A is an n X n matrix distributed by rows, b and c are replicated vectors, p is the number of processes, and ttiis proc is the process ID. A static work distribution scheme is used, and a single global communication operation is required. Each process computes the elements c, of the c vector corresponding to the locally stored rows of A, and an all-to-all broadcast operation puts a copy of the entire c vector on all processes. 

We will illustrate parallel matrix-vector multiplication algorithms using collective communication in section 6.4, and detailed examples and performance analyses of quantum chemistry algorithms employing collective communication operations can be found in sections 8.3,9.3, and 10.3. 

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