Parallel solution methods for triangular linear systems of equations

Authors:
Samuel E. Orcutt
Affiliations:
-
Venue:
Parallel solution methods for triangular linear systems of equations
Year:
1974

Citing 0
Cited 3

Practical Parallel Band Triangular System Solvers

ACM Transactions on Mathematical Software (TOMS)
Ultracomputers

ACM Transactions on Programming Languages and Systems (TOPLAS)
The Parallel Solution of Triangular Systems of Equations

IEEE Transactions on Computers

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Abstract

In this paper we consider developing parallel solution methods for triangular linear systems of equations. For a system of N equations in N unknowns the serial method requires O(N2) steps, and the straightforward parallel method requires steps and O(N) processors. In this paper we develop methods that require O(log N) time when used with O(N3) processors and O( R(N) log N) time when used with O(N2) processors. We also consider solutions to band triangular systems and develop a method that requires O((log N) (log m)) time and O(Nm2) processors, where m is the bandwidth of the system.