Iterative Methods for An Inverse Problem

Authors: Minghui Wang, Shanrui Hu

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.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1078223

References:

[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.