Generalized Scans and Tri-Diagonal Systems

Motivatedby the analysis of known parallel techniques for the solution of linear tridiagonal system, we introduce generalized scans, a class of recursively de ned lengthpreserving, sequence-to-sequence transformations that generalize the well-known pre x computations scans. Generalized scan functions are described in terms of three algorithmicphases, the reduction phase that saves data for the third or expansion phase and prepares data for the second phase which is a recursive invocation of the same function on one fewer variable. Both the reduction and expansion phases operate on bounded number of variables, a key feature for their parallelization. Generalized scans enjoy a property, called here protoassociativity, that gives rise to ordinary associativity when generalized scans are specialized to ordinary scans. We show that the solution of positive de nite block tridiagonal linear systems can be cast as a generalized scan, thereby shedding light on the underlying structure enabli...

• Type: Conference
• Year: 1995
• Where: STACS
• Authors: Paul F. Fischer, Franco P. Preparata, John E. Savage
• Keywords: Expansion Phases, Generalized Scan, STACS 1995, Theoretical Computer Science, Tridiagonal Systems