Ruhe A. Algorithms for the nonlinear eigenvalue problems[J]. SIAM J. Numer. Anal., 1973, 10: 674-689.
[2]
Sun W, Liu K M. Iterative algorithms for nonlinear ordinary differential eigenvalue problems[J]. Appl. Numer. Math., 2001, 38: 61-376.
[3]
Kim C W, Bennighof J K. Fast frequency response analysis of large-scale structures with non-proportional damping[J]. Int. J. Numer. Meth. Eng., 2007, 69: 978-992.
[4]
Bramely J S, Dennis S C R. The calculation of eigenvalues for the stationary perturbation of Poiseuille flow[J]. J. Comput. Phys., 1982, 47: 179-198.
[5]
Hu H Y, Wang Z H. Dynamics of Controlled Mechanical Systems with Delayed Feedback[M]. Springer Verlag, Berlin, 2002.
[6]
Tisseur F, Meerbergen K. The quadratic eigenvalue problem[J]. SIAM Rev., 2001, 43: 235-286.
[7]
Przemieniecki J S. Theory of Matrix Structural Analysis[M]. McGraw-Hill, New York, 1968.
[8]
Gupta K K. On a finite dynamic element method for free vibration analysis of structures[J]. Comput. Methods Appl. Mech. Eng., 1976, 9: 105-120.
[9]
Dumont N A. On the solution of generalized nonlinear complex-symmetric eigenvalue problems[J]. Int. J. Numer. Meth. Eng., 2007, 71: 1534-1568.
[10]
Conca C, Planchard J, Vanninathan M. Existence and location of eigenvalues for fluid-solid structures[J]. Comput. Methods Appl. Mech. Eng., 1989, 77: 253-291.
[11]
Voss H. A rational spectral problem in fluid-solid vibration[J]. Electro. Trans. Numer. Anal., 2003, 16: 94-106.
[12]
Su Y F, Bai Z Z. Solving rational eigenvalue problems via linearization[J]. SIAM J. Matrix. Anal. Appl., 2011, 32: 201-216.
[13]
Adhikari S, Pascual B. Eigenvalues of linear viscoelastic systems[J]. J. Sound Vib., 2009, 325: 1000-1011.
[14]
Hwang T M, Lin W W, Wang W C, Wang W. Numerical simulation of three dimensional pyramid quantum dot[J]. J. Comput. Phys., 2004, 196: 208-232.
[15]
Voss H. Numerical calculation of the electronic structure for three-dimensional quantum dots[J]. Comput. Phys. Commun., 2006, 174: 441-446.
[16]
Hwang T M, Wang W C, Wang W. Numerical schemes for three-dimensional irregular shape quantum dots over curvilinear coordinate systems[J]. J. Comput. Phys., 2007, 226: 754-773.
[17]
Mehrmann V, Voss H. Nonlinear eigenvalue problems: A challenge for modern eigenvalue methods[J]. GAMM-Mitteilungen, 2005, 27: 121-152.
[18]
Gohberg I, Lancaster P, Rodman L. Matrix Polynomials[M]. Academic Press, New York, 1982.
[19]
Higham N J, Mackey D S, Tisseur F. The conditioning of linearizations of matrix polynomials[J]. SIAM J. Matrix Anal. Appl., 2006, 28: 1005-1028.
[20]
Lancaster P. A generalised Rayleigh quotient iteration for λ-matrices[J]. Arch. Ration. Mech. Anal., 1961, 8: 309-322.
[21]
Szyld DB, Xue F. Local convergence analysis of several inexact Newton-type algorithms for general nonlinear eigenvalue problems[J]. Numer. Math., 2013, 123: 333-362.
[22]
Kublanovskaya V N. On an approach to the solution of the generalized latent value problem for λ-matrices[J]. SIAM. J. Numer. Anal., 1970, 7: 532-537.
[23]
Dai H, Bai Z Z. On smooth LU decompositions with applications to solutions of nonlinear eigenvalue problems[J]. J. Comput. Math., 2010, 28: 745-766.
[24]
Anselone P, Rall L. The solution of characteristic value-vector problems by Newton's method[J]. Numer. Math., 1968, 11: 38-45.
[25]
Jarlebring E. Convergence factors of Newton methods for nonlinear eigenvalue problems[J]. Linear Algebra Appl., 2012, 436: 3943-3953.
[26]
Neumaier A. Residual inverse iteration for nonlinear eigenvalue problem[J]. SIAM J.Numer. Anal., 1985, 22: 914-923.
[27]
Jarlebring E, Michiels W. Analyzing the convergence factor of residual inverse iteration[J]. BIT, 2011, 51: 937-957.
[28]
Voss H. An Arnoldi method for nonlinea eigenvalue problems[J]. BIT, 2004, 44: 387-401.
[29]
Sleijpen G L G, Van der Vorst H V. A Jacobi-Davidson iteration method for linear eigenvalue problems[J]. SIAM J. Matrix Anal. Appl., 1996, 17: 401-425.
[30]
Sleijpen G L G, Booten A G L, Fokkema D R, Van der Vorst H V. Jacobi-Davidson type methods for generalized eigenproblems and polynomial eigenproblems[J]. BIT, 1996, 36: 595-633.
[31]
Betcke T, Voss H. A Jacobi-Davidson-type projection method for nonlinear eigenvlaue pro-blems[J]. Future Gener. Comp. Sy., 2004, 20: 363-372.
[32]
Voss H. A Jacobi Davidson method for nonlinear and nonsymmetric eigenproblems[J]. Comput. Struct., 2007, 85: 1284-1292.
[33]
Bai Z, Su Y. SOAR: a second-order Arnoldi method for the solution of the quadratic eigenvalue problem[J]. SIAM J. Matrix Anal. Appl., 2005, 26: 640-659.
[34]
张治中. 精化迭代块二阶Arnoldi方法[D]. 南京航空航天大学硕士 学位论文, 2006.
[35]
古志鸣. 现代分析及其应用引论[M]. 北京: 科学出版社, 2004.
[36]
Betcke T, Higham N J, Mehrmann V, Schroder C, Tisseur F. NLEVP: A collection of nonlinear eigenvalue problems[J]. ACM Trans. Math. Softw., 2013, 39(2), Article 7, 28 pages.
[37]
Jain N K, Singhal K. On Kublanovskaya's approach to the solution of the generalized latent value problem for functional λ-matrices[J]. SIAM J. Numer. Anal., 1983, 20: 1062-1070.