An inverse problem of doubly center matrices is discussed. By translating the constrained problem into unconstrained problem, two iterative methods are proposed. A numerical example illustrate our algorithms.
[1] E. C. Tan, "Derivation of similar matrix of the scattering matrix for
numerical compution in electronic networks," Journal of Circuits,
Systems, and Computers (JCSC), vol. 6, pp. 599-606, Dec 1996.
[2] WANG Yansong, LIU Jun, LI Zhougshu, "Optimal configuring of
passive filters in distribution network," High Voltage Engineering, vol.
36, no. 9, pp. 2324-2328, Sep 2010.
[3] PENG Qian, JIANG Tong, YANG Yihan, "State-estimation iteration
algorithm of distribution network based on Y-matrix equation,"
Proceedings of the CSEE, vol. 28, no. 19, pp. 65-68, July 2008.
[4] CHENG Shaogeng, CUI Duwu, LIU Xiaohe, Analysis of Electronic
Network (M), Beijing: Machine Press, 1993, pp. 269-285.
[5] Zhou Shuo, WU Baisheng, "The inverse problem of center matrices and
its application to the theory of electric network," Chinese Journal of
Engineering Mathematics, vol 24, no 4, pp. 611-617, Aug 2007.
[6] WANG Songgui, YANG Zhenhai, Generalized Inverse Matrix and Its
Applications(M), Beijing Industy Press, 1996.
[7] PENG Yaxin, "The iterative method for the solutions and the optimal
approximation of the constrained matrix equation," PhD thesis, Hunan
University, Sep. 2004
[8] C. C. Paige and A. Saunders, "Lsqr: An algorithm for sparse linear
equations and sparse least squares," ACM Trans. Math.
Comput.Software, vol 8(1), pp. 43-71, June 1982.
[1] E. C. Tan, "Derivation of similar matrix of the scattering matrix for
numerical compution in electronic networks," Journal of Circuits,
Systems, and Computers (JCSC), vol. 6, pp. 599-606, Dec 1996.
[2] WANG Yansong, LIU Jun, LI Zhougshu, "Optimal configuring of
passive filters in distribution network," High Voltage Engineering, vol.
36, no. 9, pp. 2324-2328, Sep 2010.
[3] PENG Qian, JIANG Tong, YANG Yihan, "State-estimation iteration
algorithm of distribution network based on Y-matrix equation,"
Proceedings of the CSEE, vol. 28, no. 19, pp. 65-68, July 2008.
[4] CHENG Shaogeng, CUI Duwu, LIU Xiaohe, Analysis of Electronic
Network (M), Beijing: Machine Press, 1993, pp. 269-285.
[5] Zhou Shuo, WU Baisheng, "The inverse problem of center matrices and
its application to the theory of electric network," Chinese Journal of
Engineering Mathematics, vol 24, no 4, pp. 611-617, Aug 2007.
[6] WANG Songgui, YANG Zhenhai, Generalized Inverse Matrix and Its
Applications(M), Beijing Industy Press, 1996.
[7] PENG Yaxin, "The iterative method for the solutions and the optimal
approximation of the constrained matrix equation," PhD thesis, Hunan
University, Sep. 2004
[8] C. C. Paige and A. Saunders, "Lsqr: An algorithm for sparse linear
equations and sparse least squares," ACM Trans. Math.
Comput.Software, vol 8(1), pp. 43-71, June 1982.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:60974", author = "Minghui Wang and Shanrui Hu", title = "Iterative Methods for An Inverse Problem", abstract = "An inverse problem of doubly center matrices is discussed. By translating the constrained problem into unconstrained problem, two iterative methods are proposed. A numerical example illustrate our algorithms.
", keywords = "doubly center matrix, electric network theory,iterative methods, least-square problem.", volume = "5", number = "4", pages = "649-3", }
