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2016, Vol. 36 No. 2   Published date: 30 June 2016
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• An Inexact Broyden Method for Nonlinear Equations

  Wu Peiyu, Zhang Li

  2016, 36(2): 1-9. doi:

  Abstract ( 1074 )   PDF (447KB) ( 82 )   　　

  This paper introduces an inexact Broyden method for solving nonlinear equations,which is an extension of the method in[8].Under appropriate conditions,we prove that the proposed method converges globally and superlinearly.Numerical results are given to show its efficiency.

• Constructing a Symmetric Tridiagonal Matrix Based on Its Defective Generalized Eigenpair and Nonleading Principle Submatrix

  Zhu Qundi, Hong Pingzhou, Huang Xiantong

  2016, 36(2): 10-21. doi:

  Abstract ( 1150 )   PDF (429KB) ( 99 )   　　

  In this paper we consider the equation AnX =λCnX ,where Anis a symmetric tridiagonal matrix and Cnis a diagonal matrix.Regarding Anas a 3×3blocked matrix,given a(r+1)×(r+s)non-sequential principle submatrix of An ,given Cn ,four vectors X1 = (x1,…,xr)＇,X3=(xr+s+1,…,xn)＇,Y1 = (y1,…,yr)＇,Y3=(yr+s+1,…,yn)＇and two distinct real numbersλ,μ,we construct a symmetric tridiagonal matrix Anand two vectors X2 = (xr+1,…,xr+s)＇,Y2= (yr+1,…,yr+s)＇such that AnX =λCn X and AnY =μCn Y ,where X = (X1＇, X2＇,X3＇)＇,Y = (Y1＇,Y2＇,Y3＇)＇.The existence conditions such that the problem has a solution and the corresponding algorithm to find the solutions are given.A numerical example is presented to show the validity of the algorithm.

• The Maximum Value for the Harary Index of Unicyclic Graphs with a Given Girth

  Chen Dandan

  2016, 36(2): 22-27. doi:

  Abstract ( 973 )   PDF (234KB) ( 107 )   　　

  In this paper,we first give a formula for calculating the Harary index of a unicyclic graph according to the structure,and then using this formula,we obtain the maximum value for the Harary index of unicyclic graphs with a given girth,and characterize the extremal graph with respect to the Harary index.