アフィン演算
(Affine arithmetic から転送)
出典: フリー百科事典『ウィキペディア（Wikipedia）』 (2022/10/30 21:20 UTC 版)
数値解析・精度保証付き数値計算においてアフィン演算（アフィンえんざん、英: affine arithmetic）は区間演算における区間幅の増大を抑止するために作られた演算方式である[1]。
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- ^ Y. Kanazawa and S. Oishi (2002), "A numerical method of proving the existence of solutions for nonlinear ODEs using affine arithmetic". Proc. SCAN'02 — 10th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics.
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- ^ F. Messine (2002), "Extensions of affine arithmetic: Application to unconstrained global optimization". Journal of Universal Computer Science, 8 11, 992–1015.
- ^ Grimm, C., Heupke, W., & Waldschmidt, K. (2004, February). Refinement of mixed-signals systems with affine arithmetic. In Proceedings Design, Automation and Test in Europe Conference and Exhibition (Vol. 1, pp. 372-377). IEEE.
- ^ Grimm, C., Heupke, W., & Waldschmidt, K. (2004). Analysis of mixed-signal systems with affine arithmetic. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 24(1), 118-123.
- ^ Radojicic, C., Grimm, C., Schupfer, F., & Rathmair, M. (2013). Verification of mixed-signal systems with affine arithmetic assertions. VLSI Design, 2013, 5.
- ^ Radojicic, C., & Grimm, C. (2016, June). Formal verification of mixed-signal designs using extended affine arithmetic. In 2016 12th Conference on Ph. D. Research in Microelectronics and Electronics (PRIME) (pp. 1-4). IEEE.
- ^ Vaccaro, A., Canizares, C. A., & Villacci, D. (2009). An affine arithmetic-based methodology for reliable power flow analysis in the presence of data uncertainty. IEEE Transactions on Power Systems, 25(2), 624-632.
- ^ Gu, W., Luo, L., Ding, T., Meng, X., & Sheng, W. (2014). An affine arithmetic-based algorithm for radial distribution system power flow with uncertainties. International Journal of Electrical Power & Energy Systems, 58, 242-245.
- ^ Wang, S., Han, L., & Wu, L. (2014). Uncertainty tracing of distributed generations via complex affine arithmetic based unbalanced three-phase power flow. IEEE Transactions on Power Systems, 30(6), 3053-3062.
- ^ Pirnia, M., Cañizares, C. A., Bhattacharya, K., & Vaccaro, A. (2014). A novel affine arithmetic method to solve optimal power flow problems with uncertainties. IEEE Transactions on Power Systems, 29(6), 2775-2783.
- ^ Vaccaro, A., & Canizares, C. A. (2016). An affine arithmetic-based framework for uncertain power flow and optimal power flow studies. IEEE Transactions on Power Systems, 32(1), 274-288.
- ^ Ding, T., Bo, R., Guo, Q., Sun, H., Wu, W., & Zhang, B. (2013). A non-iterative affine arithmetic methodology for interval power flow analysis of transmission network.
- ^ Ding, T., Cui, H., Gu, W., & Wan, Q. (2012). An uncertainty power flow algorithm based on interval and affine arithmetic. Automation of Electric Power Systems, 13.
- ^ Pirnia, M., Cañizares, C. A., Bhattacharya, K., & Vaccaro, A. (2012, July). An affine arithmetic method to solve the stochastic power flow problem based on a mixed complementarity formulation. In 2012 IEEE Power and Energy Society General Meeting (pp. 1-7). IEEE.
- ^ 三島和博. (2011). アフィン演算を用いた非線形回路のすべての解を求めるアルゴリズム. 中央大学大学院研究年報 理工学研究科編, 41.
- ^ 小林玄宙, 三島和博, & 山村清隆. (2012). A-2-14 アフィン演算と LP 縮小を用いた非線形回路の全解探索法 (A-2. 非線形問題, 一般セッション). 電子情報通信学会総合大会講演論文集, 2012, 59.
- ^ Femia, N., & Spagnuolo, G. (2000). True worst-case circuit tolerance analysis using genetic algorithms and affine arithmetic. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 47(9), 1285-1296.
- ^ Lemke, A., Hedrich, L., Barke, E., & Barke, E. (2002, November). Analog circuit sizing based on formal methods using affine arithmetic. In Proceedings of the 2002 IEEE/ACM international conference on Computer-aided design (pp. 486-489). ACM.
- ^ Ding, T., Trinchero, R., Manfredi, P., Stievano, I. S., & Canavero, F. G. (2015). How affine arithmetic helps beat uncertainties in electrical systems. IEEE Circuits and Systems Magazine, 15(4), 70-79.
- ^ Liao, X., Liu, K., Le, J., Zhu, S., Huai, Q., Li, B., & Zhang, Y. (2020). Extended affine arithmetic-based global sensitivity analysis for power flow with uncertainties. International Journal of Electrical Power & Energy Systems, 115, 105440.
- ^ IRDB:00931/0000195611
- ^ Messine, F., & Touhami, A. (2006). A general reliable quadratic form: An extension of affine arithmetic. Reliable Computing, 12(3), 171-192.
- ^ Goubault, E., & Putot, S. (2008). Perturbed affine arithmetic for invariant computation in numerical program analysis. arXiv preprint arXiv:0807.2961.
- ^ Shou, H., Lin, H., Martin, R., & Wang, G. (2003). Modified affine arithmetic is more accurate than centered interval arithmetic or affine arithmetic. In Mathematics of Surfaces (pp. 355-365). Springer, Berlin, Heidelberg.
- ^ Shou, H., Lin, H., Martin, R. R., & Wang, G. (2006). Modified affine arithmetic in tensor form for trivariate polynomial evaluation and algebraic surface plotting. en:Journal of computational and applied mathematics, 195(1-2), 155-171.
[続きの解説]
「アフィン演算」の続きの解説一覧
- 1 アフィン演算とは
- 2 アフィン演算の概要
- 3 参考文献
- 4 外部リンク
- アフィン演算のページへのリンク
