• 论文 •

### 求解对称非线性矩阵特征值问题的一个三阶收敛的算法

1. 中国科学院沈阳计算所 ;中国科学院沈阳计算所
• 出版日期:1992-02-20 发布日期:1992-02-20

### A CUBICALLY CONVERGENT ALGORITHM FOR THE REAL SOLUTION OF THE GENERALIZED LATENT VALUE PROBLEM FOR SYMMETRIC FUNCTIONAL LAMBDA-MATRICES

1. Chen Guang-yi;Xue Yan-cai Shenyang Institute of Computing Technology
• Online:1992-02-20 Published:1992-02-20

A cubically convergent algorithm is presented for solving the nonlinear eigenvalue problemA(λ)x= 0, x≠0, where A(λ) is a symmetric functional Lambda-matrix. The amount of com-putation is essentially the same as that of the usually used quadratically convergent algorithm,but the order of convergence is higher. What is more, this algorithm is better than Lancaster'scubically convergent algorithm. Numerical examples are also given.
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 [1] J. H. Wilkinson, The algebraic eigenvalue problem, Clarendon Press, Oxford,1965． [2] P. Lancaster, Lambda-matrices and vibrating system, Pergamon Press, Oxford, 1966． [3] Sun Ji-Guang, Eigenvalues and eigenvectors of a matrix dependent on several parameters, J.Comp. Math. 3(1985) , 351-364． [4] 孙继广,矩阵扰动分析,科学出版社,1987． [5] A. Ruhe. Algorithms for the nonlinear eigenvalue problem, SIAM J. Numer. Anal.10(1973) ,674-689． [6] A. Neumaier, Residual inverse iteration for the nonlinear eigenvalue problem,SIAM J.Numer.Anal,22(1985) , 914-923．
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