Hostname: page-component-848d4c4894-ttngx Total loading time: 0 Render date: 2024-05-05T20:28:17.636Z Has data issue: false hasContentIssue false
  • English
  • Français

Inverse multiparameter eigenvalue problems for matrices II

Published online by Cambridge University Press:  20 January 2009

Patrick J. Browne  and
B. D. Sleeman
Patrick J. Browne
Affiliation:
Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada, T2N 1N4
B. D. Sleeman
Affiliation:
Department of Mathematical Sciences, University of Dundee, Dundee DD1 4H4
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This is a sequel to our previous paper [4] where we initiated a study of inverse eigenvalue problems for matrices in the multiparameter setting. The one parameter version of the problem under consideration asks for conditions on a given n × n symmetric matrix A and on n given real numbers s1≦s2≦…≦sn under which a diagonal matrix V can be found so that A + V has sl,…,sn as its eigenvalues. Our motivation for this problem and our method of attack on it in [4]p comes chiefly from the work of Hadeler [5] in which sufficient conditions were given for existence of the desired diagonal V. Hadeler's approach in [5] relied heavily on the Brouwer fixed point theorem and this was also our main tool in [4]. Subsequently, using properties of topological degree, Hadeler [6] gave somewhat different conditions for the existence of the diagonal V. It is our desire here to follow this lead and to use degree theory to give some results extending those in [6] to the multiparameter case.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 29 , Issue 3 , October 1986 , pp. 343 - 348
Copyright
Copyright © Edinburgh Mathematical Society 1986

References

REFERENCES

1.Blum, E. K., Numerical Analysis and Computation, Theory and Practice (Addison-Wesley, Reading, Mass., 1972).Google Scholar
2.Binding, P. and Browne, P. J., Spectral properties of two-parameter eigenvalue problems, Proc. Roy. Soc. Edinburgh 89A (1981), 157–173.Google Scholar
3.Browne, P. J., Multiparameter problems: The last decade, Proceedings 1982 Dundee Conference on Ordinary and Partial Differential Equations(Springer-Verlag Lecture Notes in Mathematics, Vol. 1964), 95–109.Google Scholar
4.Browne, P. J. and Sleeman, B. D., Inverse multiparameter eigenvalue problems for matrices, Proc. Roy. Soc. Edinburgh 100 A (1985), 29–38.CrossRefGoogle Scholar
5.Hadeler, K. P., Ein inverses eigenwertproblem, Lin. Alg. and Appns. 1 (1968), 83–101.Google Scholar
6.Hadeler, K. P., Existenz- und eindeutigkeitssatze fur inverse eigenwertaufgaben mit hilfe des topologischen abbildungsgrades, Arch. Rational Mech. Anal. 42 (1971), 317–322.CrossRefGoogle Scholar