Abstract
It is required to determine a diagonal matrix X such that the symmetric matrix A+X has preassigned eigenvalues (the additive problem). An iteration process is described that is based on the use of two-dimensional rotations, and convergence problems are analyzed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
K. P. Hadeler, “Ein inverses Eigenwertproblem,” Linear Algebra and Its Applications,1, 83–101 (1968).
Francoise Laborde, “Sur un probleme inverse d'un probleme de valeurs propres,” C. R. Acad. Sci. Paris,268, 153–156 (1969).
G. H. De Oliveira, “Note on an inverse characteristic value problem,” Num. Math.,15, 345–347 (1970).
G. N. De Oliveira, “Note on the additive inverse eigenvalue problem,” Rev. Fac. C. Lisboa,13, 21–26 (1970).
D. K. Faddeev and V. N. Faddeeva, Computational Methods of Linear Algebra, W. H. Freeman, San Francisco (1963).
M. Marcus and H. Minc, Survey of Matrix Theory and Matrix Inequalities [Russian translation], Moscow (1972).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 48, pp. 12–17, 1974.
Rights and permissions
About this article
Cite this article
Kublanovskaya, V.N. The solution of the additive eigenvalue problem of matrices. J Math Sci 10, 647–651 (1978). https://doi.org/10.1007/BF01083965
Issue Date:
DOI: https://doi.org/10.1007/BF01083965