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IADIS International Conference WWW/Internet 2010calculation. Additionally, we have another important evidence from both tables of our experiment. It is alsoconfirmed that speedup improvement has been approximately achieved in proportion of the numbers ofworker process. Our experiment did demonstrate that our two cases of parallel programming are suitableenough to explain validity of Amdahl's law. These are considered to be practical and important examples forbeginners to understand introductory parallel programming in the real educational environment.5. CONCLUSIONThis paper has described some samples of parallel programming based on Master-worker Paradigm and theirevaluation. We have compared the computer algebra system Risa/Asir to Cell B.E. with SPE library throughpractical experience. This is why education about parallel programming becomes important as several kindsof multiple computer and processors are available for users by means of the Internet and Cloud computing.An advantage of Risa/Asir is to utilize the same program on multi-core processor as well as clusteredcomputers. SPE library is a special one for using SPE of Cell B.E. and users need POSIX thread libraries inorder to execute multiples of SPEs as "workers" simultaneously. So it is indispensable to realize some kindsof TCP/IP-based communication between each machine in PLAYSTATION3-based cluster system.With regard to numerical analysis, Risa/Asir cannot be compared to Cell B.E. with SPE library, because itis not designed as an efficient software for numerical computation. It is confirmed that Risa/Asir is suitablefor symbolic and/or algebraic computation and is not good at high-speed computation. By the way, we havealso ascertained the qualitative capability of Risa/Asir to describe parallel programming based on MasterworkerParadigm through our experiment.In the future works, we will try to utilize high-speed computation with 128-bit Vector/ SIMD processingunits of SPEs. We have some problems to improve computation performance. Through a real experiment, itis confirmed that one of them is related to realize a smart DMA (Direct Memory Access) between the mainmemory of Cell B.E. and local memories of SPEs. If such a DMA procedure is less complicated, users willbe able to achieve parallel programming more powerfully and effectively.ACKNOWLEDGEMENTSThe authors are thankful to Professor Hitoshi Inomo, and Professor Wataru Shiraki of Kagawa University fortheir continuous supports. This study was partly supported by the Special Science Fund from Cmicroincorporated in Japan and also partly supported by Research for Promoting Technological Seeds from JapanScience and Technology Agency (JST).REFERENCES[1] Hennessy, J.L. and Patterson, D.A. 2003, Computer Architecture: A Quantitative Approach (third Edition). MorganKaufmann.[2] Amdahl, G.M., 1967. Validity of the Single-Processor Approach to Achieving Large Scale Computing Capabilities.Validity of the Single-Processor Approach to Achieving Large Scale Computing Capabilities. In AFIPS ConferenceProceedings, pp. 483–485.[3] Hill,M. and Marty, M.R. 2008, Amdahl's law in the multicore era, IEEE Computer, vol. 41, no. 7, pp.33-38.[4] Sun,X-H. And Chen,Y. 2010, Reevaluating Amdahl's law in the multicore era, Journal of Parallel and DistributedComputing. Vol.70, pp.183-188.[5] Wilkinson, B. and Allen, M., 1999. Parallel Programming, Prentice-Hall.[6] Shiraishi,K., et.al., 2001. On Load Balancing based on Parallelization of Wu's method, Report of Research Institutefor Mathematical Sciences, Kyoto University, Vol.1199, pp. 10-19 (in Japanese).[7] Liu, C.L., 1985. Elements of Discrete Mathematics (second Edition), McGraw-Hill.[8] Risa/Asir http://www.math.kobe-u.ac.jp/Asir/asir.html[9] Kahl, J.A., Day, M.N., Hofstee, H.P., Johns, C.R., Maeurer, T.R. and Shippy, D., 2005, Introduction to the CellMultiprocessor. IBM Journal of Research and Development, vol. 49, no. 4, pp.589-604.261