Abstract
Fitting curve is a critical problem in many testing equipment and detection system. But there was larger relative error in fitting curve when the independent variable was relatively small. In this paper, Fitting curve is formulated to a constrained linear programming. a neural dynamics optimization algorithm is obtained by considering the problem in its dual space, and then the dynamic neural network is designed to solve the optimization problem recurrently. The experimental results show that the polynomial coefficients solved by the method is stable, compared with the least square method, the relative error is obviously reduced; The method is simple and requires less samples. It provides a new simple and accurate method of curve fitting for the quantitative detection.
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References
Mathews, J.H., Fink, K.D.: Numerical Methods Using MATLAB. Prentice Hall, USA (1998)
Xiao, Y.H., Hu, Q.J.: Subspace Barzilai-Borwein gradient method for large-scale bound constrained optimization. Appl. Math. Optim. 58(2), 275–290 (2008)
Andretta, M., Birgin, E.G., Martinez, J.M.: Practical active-set euclidian trust-region method with spectral projected gradients for bound-constrained minimization. Optimization 54(3), 305–325 (2005)
Birgin, E.G., Martinez, J.M., Raydan, M.: Nonmonotone spectral projection gradient methods on convex sets. SIAM J. Optim. 10, 1196–1211 (2000)
Birgin, E.G., Martinez, J.M.: A box-constrained optimization algorithm with negative curvature directions and spectral projected gradients. In: Alefeld, G., Chen, X. (eds.) Topics in Numerical Analysis. Computing Supplementa, vol. 15, pp. 49–60. Springer, Vienna (2001)
Hopfield, J.J., Tank, D.W.: Neural computation of decisions in optimization problems. Biol. Cybern. 52, 141–152 (1985)
Xia, Y.: A new neural network for solving linear and quadratic programming problems. IEEE Trans. Neural Netw. 7(6), 1544–1548 (1996)
Malek, A., Alipour, M.: Numerical solution for linear and quadratic programming problems using a recurrent neural network. Appl. Math. Comput. 192(1), 27–39 (2007)
Rahman, S.A., Ansari, M.S.: A neural circuit with transcendental energy function for solving system of linear equations. Analog Integr. Circ. Sig. Process. 66, 433–440 (2011)
Xia, Y., Wang, J., Fork, L.M.: Grasping force optimization for multifingered robotic hands using a recurrent neural network. IEEE Trans. Robot. Autom. 20, 549–554 (2004)
Xia, Y., Chen, T., Shan, J.: A novel iteration method for computing generalized inverse. Neural Comput. 26, 449–465 (2014)
Liu, Q., Wang, J.: Finite-time convergent recurrent neural network with a hard-limiting activation function for constrained optimization with piecewise-linear objective functions. IEEE Trans. Neural Netw. 22(4), 601–613 (2011)
Acknowledgments
This work is partially supported by National Natural Foundation Project (61304199), The Ministry of science and technology projects for Hong Kong and Maco (2012DFM30040), Major projects in Fujian Province (2013HZ0002-1, 2014YZ0001).
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Xiong, B., Gan, Z., Zou, F., Gao, Y., Du, M. (2017). Curve Fitting Based on Neural Dynamics Optimization. In: Pan, JS., Lin, JW., Wang, CH., Jiang, X. (eds) Genetic and Evolutionary Computing. ICGEC 2016. Advances in Intelligent Systems and Computing, vol 536. Springer, Cham. https://doi.org/10.1007/978-3-319-48490-7_3
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DOI: https://doi.org/10.1007/978-3-319-48490-7_3
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