Abstract
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.
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Notes
- 1.
- 2.
Although the matrix data analysis method for quality control is sometimes taken to refer specifically to “principal component analysis,” it is interpreted in a broader sense in this study.
- 3.
This diagram only is the result of not designating “-saamg_ unsymtrue” in the Lis SA-AMG parameter. In the other diagrams, “-saamg _unsymtrue” is designated. Due to the existence of this option, there is no major change in the position of cells which become gray color, and there is almost no effect on the discussion in this section.
- 4.
After the lis-1.2.0 version, the problem of these two solvers was modified.
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Acknowledgments
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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Itoh, S., Sugihara, M. (2011). Systematic Performance Evaluation of Linear Solvers Using Quality Control Techniques. In: Naono, K., Teranishi, K., Cavazos, J., Suda, R. (eds) Software Automatic Tuning. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6935-4_9
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