Systematic Performance Evaluation of Linear Solvers Using Quality Control Techniques

  • Shoji ItohEmail author
  • Masaaki Sugihara


A performance evaluation framework for the solution schemes for sparse linear systems is proposed. The framework systematically constructs a performance database that provides a visual diagram of solution algorithms’ performance and characteristics to represent the relationship between the solution algorithms and solution problems. In addition, the database model is best used with software engineering techniques to facilitate automatic tuning of sparse linear solvers. This approach resembles the techniques used in quality control. Two types of cases using this approach are presented. One involves knowledge discovery in a database and reveals that preconditioning is more effective than the choice of solver for obtaining rapid convergence of iterative solutions. The other case is an improvement in quality related to numerical solving processes.

Automatic performance tuning Knowledge discovery in database Linear equations Linear solver and its preconditioning Numerical algorithm selection 



The first author (S.I.) sincerely expresses his gratitude to the members of the Japanese Automatic Tuning Research Group for their valuable discussions with him. He also extends his gratitude to Dr. Hisashi Kotakemori of TCAD International, Inc. for his valuable advice regarding programming with the Lis library. This work is partially supported by Grant-in-Aid for Scientific Research (B) “Development of the Framework to Support Large-scale Numerical Simulation on Multi-platform,” No.21300017; Grant-in-Aid for Scientific Research (B) “Development of Auto-tuning Specification Language Towards Manycore and Massively Parallel Processing Era,” No. 21300007; and Grant-in-Aid for Scientific Research (B) “A study on Autotuning enhanced by Hierarchical Algorithm Selections,” No. 20300007 of MEXT Japan; and the “Next-Generation Integrated Simulation of Living Matter” of RIKEN.


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Copyright information

© Springer New York 2011

Authors and Affiliations

  1. 1.Information Technology CenterThe University of TokyoTokyoJapan

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