A numerical method for solving inverse eigenvalue problems

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1. [1] G. Alefeld, A. Gienger and G. Mayer, Numerical validation for an inverse matrix eigenvalue problem. Computing 53 (1984) 311-322. Zbl0813.65076MR1308769
2. [2] F.W. Biegler-König, Sufficient conditions for the solubility of inverse eigenvalue problems. Linear Algebra Appl. 40 (1981) 89-100. Zbl0473.15006MR629609
3. [3] F.W. Biegler-König, A Newton iteration process for inverse eigenvalue problems. Numer. Math. 37 (1981) 349-354. Zbl0458.65023MR627109
4. [4] Z. Bohte, Numerical solution of the inverse algebraic eigenvalue problem. Comput. J. 10 (1968) 385-388. Zbl0167.45303MR221744
5. [5] Z.H. Cao, J.J. Xie and R.C. Li, A sharp version of Kahan's theorem on clustered eigenvalues. Linear Algebra Appl. 245 (1996) 147-156. Zbl0860.15017MR1404174
6. [6] X. Chen and M.T. Chu, On the least squares solution of inverse eigenvalue problems. SIAM J. Numer. Anal. 33 (1996) 2417-2430. Zbl0864.65021MR1427471
7. [7] M.T. Chu, Soiving additive inverse eigenvalue problem for symmetrie matrices by the homotopy method. IMA J.Numer. Anal. 9 (1990) 331-342. Zbl0703.65024MR1068196
8. [8] H. Dai, On the additive inverse eigenvalue problem. Transaction of Nanjing University of Aeronautics and Astronautics 7 (1990) 108-113. Zbl0737.65032
9. [9] H. Dai, Sufficient condition for the solubility of an algebraic inverse eigenvalue problem (in Chinese). Math. Numer. Sinica 11 (1989) 333-336. Zbl0687.15008MR1037457
10. [10] H. Dai and P. Lancaster, Numerical methods for finding multiple eigenvalues of matrices depending on parameters. Numer. Math. 76 (1997) 189-208. Zbl0873.65034MR1440120
11. [11] A.C. Downing and A.S. Householder, Some inverse characteristic value problems. J. Assoc. Comput. Mach. 3 (1956)203-207. MR83817
12. [12] S. Friedland, Inverse eigenvalue problems. Linear Algebra Appl. 17 (1977) 15-51. Zbl0358.15007MR472861
13. [13] S. Friedland, J. Nocedal and M.L. Overton, The formulation and analysis of numerical methods for inverse eigenvalue problems. SIAM J. Numer. Anal. 24 (1987) 634-667. Zbl0622.65030MR888754
14. [14] G.H. Golub and C. F. Van Loan, Matrix Computations, 2nd edn. Johns Hopkins University Press, Baltimore, MD (1989). Zbl0733.65016MR1002570
15. [15] K.P. Hadeler, Ein inverses Eigenwertproblem. Linear Algebra Appl. 1 (1968) 83-101. Zbl0159.03602MR227189
16. [16] W.N. Kublanovskaya, On an approach to the solution of the inverse eigenvaiue problem. Zap. Naucn. Sem. Leningrad Otdel. Mat. Inst. Steklov. (1970) 138-149. Zbl0247.65027
17. [17] F. Laborde, Sur un problème inverse d'un problème de valeurs propres. C.R. Acad. Sci. Paris. Sér. A-B 268 (1969) 153-156. Zbl0174.47001MR241441
18. [18] P. Lancaster and M. Tismenetsky, The Theory of Matrices with Applications. Academic Press, New York (1985). Zbl0558.15001MR792300
19. [19] L.L. Li, Some sufficient conditions for the solvability of inverse eigenvalue problems. Linear Algebra Appl. 148 (1991) 225-236. Zbl0725.15006MR1090762
20. [20] L.L. Li, Sufficient conditions for the solvability of algebraic inverse eigenvalue problems. Linear Algebra Appl. 221(1995) 117-129. Zbl0827.15005MR1331794
21. [21] R.C. Li, QR decomposition and nonlinear eigenvalue problems (in Chinese). Math. Numer. Sinica 14 (1989) 374-385. Zbl0997.65527
22. [22] R.C. Li, Compute multiply nonlinear eigenvalues. J. Comput. Math. 10 (1992) 1-20. Zbl0752.65042MR1159618
23. [23] R.C. Li, Algorithms for inverse eigenvalue problems. J. Comput. Math. 10 (1992) 97-111. Zbl0751.65027MR1159625
24. [24] P. Morel, Des algorithmes pour le problème inverse des valeur propres. Linear Algebra Appl. 13 (1976) 251-273. Zbl0353.65021MR395187
25. [25] M. Ortega and W.C. Rheinbold, Iterative Solution of Nonlinear Equations in Several Variables.. Academic Press New York (1970). Zbl0241.65046MR273810
26. [26] G.W. Stewart and J.-G. Sun, Matrix Perturbation Analysis. Academic Press, New York (1990). MR1061154
27. [27] J.-G. Sun, On the sufficient conditions for the solubility of algebraic inverse eigenvalue problems (in Chinese). Math. Numer. Sinica 9 (1987) 49-59. Zbl0616.15012MR893378
28. [28] J.-G. Sun and Q. Ye, The unsolvability of inverse algebraic eigenvalue problems almost everywhere. J. Comput.Math. 4 (1986) 212-226. Zbl0595.15007MR860150
29. [29] J.-G. Sun, The unsolvability of multiplicative inverse eigenvalues almost everywhere. J. Comput. Math. 4 (1986) 227-244. Zbl0595.15008MR860151
30. [30] S.F. Xu, On the necessary conditions for the solvability of algebraic inverse eigenvalue problems. J. Comput. Math. 10 (1992) 93-97. Zbl0745.15004
31. [31] S.F. Xu, On the sufficient conditions for the solvability of algebraic inverse eigenvalue problems. J. Comput. Math. 10 (1992) 171-180. Zbl0745.15005
32. [32] Q. Ye, A class of iterative algorithms for solving inverse eigenvalue problems (in Chinese). Math. Numer. Sinica 9(1987) 144-153. Zbl0633.65037MR915302
33. [33] S.Q. Zhou and H. Dai, The Algebraic Inverse eigenvalue Problem (in Chinese). Henan Science and Technology Press, Zhengzhou, China (1991).