Applied Parallel Computing. State of the Art in Scientific Computing

Volume 3732 of the series Lecture Notes in Computer Science pp 740-746

Performance Tuning of Matrix Triple Products Based on Matrix Structure

  • Eun-Jin ImAffiliated withLancaster UniversityKookmin University
  • , Ismail BustanyAffiliated withCarnegie Mellon UniversityBarcelona Design Inc
  • , Cleve AshcraftAffiliated withCarnegie Mellon UniversityLivermore Software Technology Corporation
  • , James W. DemmelAffiliated withCarnegie Mellon UniversityU.C. Berkeley
  • , Katherine A. YelickAffiliated withCarnegie Mellon UniversityU.C. Berkeley

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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.