[1] 杨爱利, 伍渝江, 李旭, 等. 一类非线性方程组的Newton-PSS迭代法术[J]. 计算数学, 2012, 34(4):329-340.[2] 陈传淼, 胡宏伶, 雷蕾, 等. 非线性方程组的Newton流线法[J]. 计算数学, 2012, (3):235-258.[3] Yamamoto T. Historical developments in convergence analysis for Newton's and Newton-like methods[J]. J. Comput. Appl. Math., 2000, 124(1):1-23.[4] Chun C. A family of composite fourth-order iterative methods for solving nonlinear equations[J]. Appl. Math. Comput., 2007, 187(2):951-956.[5] Meyer G H. On solving nonlinear equations with a one-parameter operator imbedding[J]. SIAM J. Nuner. Anal., 1969, 5(4):739-752.[6] 李庆扬, 莫孜中, 祁力群. 非线性方程组的数值解法[M]. 北京:科学出版社, 1987.[7] Decker D W, Kelley C T. Convergence rates for Newton's method at singular points[J]. SIAM J. Nuner. Anal., 1983, 20(2):296-314.[8] Weber H, Werner W. On the accurate determination of nonisolated solutions of nonlinear equations[J]. Computing, 1981, 26(4):315-326.[9] 杨柳, 陈艳萍. 一种新的Levenberg-Marquardt算法的收敛性[J]. 计算数学, 2005, 27(1):55-62.[10] 李受百. 函数因子法-非线性方程组求解中处理奇异问题的一种新方法[J]. 计算数学, 1983, 5(2):162-175.[11] 夏林林, 吴开腾. 大范围求解非线性方程组的指数同伦法[J]. 计算数学, 2014, 2(2):215-224.[12] Wu X. Note on the improvement of Newton's method for system of nonlinear equations[J]. Appl. Math. Comput., 2007, 189(2):1476-1479.[13] Kou J, Li Y, Wang X. Efficient continuation Newton-like method for solving systems of non-linear equations[J]. Appl. Math. Comput., 2006, 174(2):846-853.[14] Hueso J L, Martínez E, Torregrosa J R. Modified Newton's method for systems of nonlinear equations with singular jacobian[J]. J. Comput. Appl. Math., 2009, 224(1):77-83.[15] Peris R, Marquina A, Candela V. The convergence of the perturbed Newton method and its application for ill-conditioned problems[J]. Appl. Math. Comput., 2011, 218(7):2988-3001.[16] Ortega J M, Rheinboldt W C. Iterative solution of nonlinear equations in several variables[M]. New York:Academic Press, 1970.[17] 黄象鼎, 曾钟钢, 马亚楠. 非线性数值分析的理论与方法[M]. 武汉:武汉大学出版社, 2004.[18] 李庆扬. 解非线性方程组的离散型延拓法[J]. 数值计算与计算机应用, 1984, 5(2):114-124. |