Performance Tuning of Matrix Triple Products Based on Matrix Structure
- Cite this paper as:
- Im EJ., Bustany I., Ashcraft C., Demmel J.W., Yelick K.A. (2006) Performance Tuning of Matrix Triple Products Based on Matrix Structure. In: Dongarra J., Madsen K., Waśniewski J. (eds) Applied Parallel Computing. State of the Art in Scientific Computing. PARA 2004. Lecture Notes in Computer Science, vol 3732. Springer, Berlin, Heidelberg
Sparse matrix computations arise in many scientific and engineering applications, but their performance is limited by the growing gap between processor and memory speed. In this paper, we present a case study of an important sparse matrix triple product problem that commonly arises in primal-dual optimization method.
Instead of a generic two-phase algorithm, we devise and implement a single pass algorithm that exploits the block diagonal structure of the matrix. Our algorithm uses fewer floating point operations and roughly half the memory of the two-phase algorithm. The speed-up of the one-phase scheme over the two-phase scheme is 2.04 on a 900 MHz Intel Itanium-2, 1.63 on an 1 GHz Power-4, and 1.99 on a 900 MHz Sun Ultra-3.
Unable to display preview. Download preview PDF.