Condiciones para el problema aditivo inverso de autovalor.
DOI:
https://doi.org/10.22199/S07160917.1990.0016.00001Keywords:
Vector, Autovalor, Funciones, AlgortimosAbstract
En este trabajo discutimos condiciones necesarias y condiciones suficientes para la solución del siguiente problema inverso de autovalor: Cada una matriz real simétrica A de orden n x n y un conjunto de números reales {?i}7, encontrar una matriz diagonal real D tal que A + D tiene autovalores ?i.
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References
BIEGLER-KONIG, F.W. Sufficient Conditions for the Solvability of Inverse Eigenvalue Problems. Linear Algebra and Its Applications 40: 89-100, 1981.
DE OLIVEIRA, G.N. Note on an Inverse Characteristic Value Problem. Numerische Mathematik 15: 345-347, 1970.
____. Matrix Inequalities and the Additive Inverse Eigenvalue Problem. Computing 9: 95-100, 1972.
DOWNING, A.C., Jr. and HOUSEHOLDER, A.S. Sorne Inverse Characteristic Value Problems. Journal Assoc. for Computing Machinery 3: 203-207, 1956.
FRIEDLAND, S., and MELKMAN, A.A. On the Eigenvalues of Non-negative Jacobi Matrices. Linear Algebra and Its Applications 25: 239-253, 1979.
HADELER, K.P. Ein Inverses Eigenwertproblem. Linear Algebra and lts Applications 1: 83-101, 1968.
HOFFMAN, A., and WIELANDT, H. The Variation of the Spectrum of a Normal Matrix. Duke Math. Journal 20: 37-40, 1953.
KATO, T. Perturbation Theory for Linear Operators. Springer-Verlag New York, Inc., 1966.
LABORDE, F. Sur un Probleme Inverse d'un Probleme de Valeurs Propres. C.R. Acad. Sc. París 268: 153-156, 1969.
MIRSKY, L. The Spread of a Matrix. Mathematics 3: 127-130, 1956.
MOREL, P. A Propos d'un Probleme Inverse de Valeurs Propres. C.R. Acad. Sc. París 277: 125-128, 1973.
___. Sur le Probleme Inverse des Valeurs Propes. Numerisehe MathematTk 23: 83-94, 1974.
___. Des Algorithmes pour le Probleme Inverse des Valeurs Propres. Linear Algebra and its Applications 13: 251-273, 1976.
WILKINSON, J.H. The Algebraic Eigenvalue Problem. Oxford University Press, London, 1965.
DE OLIVEIRA, G.N. Note on an Inverse Characteristic Value Problem. Numerische Mathematik 15: 345-347, 1970.
____. Matrix Inequalities and the Additive Inverse Eigenvalue Problem. Computing 9: 95-100, 1972.
DOWNING, A.C., Jr. and HOUSEHOLDER, A.S. Sorne Inverse Characteristic Value Problems. Journal Assoc. for Computing Machinery 3: 203-207, 1956.
FRIEDLAND, S., and MELKMAN, A.A. On the Eigenvalues of Non-negative Jacobi Matrices. Linear Algebra and Its Applications 25: 239-253, 1979.
HADELER, K.P. Ein Inverses Eigenwertproblem. Linear Algebra and lts Applications 1: 83-101, 1968.
HOFFMAN, A., and WIELANDT, H. The Variation of the Spectrum of a Normal Matrix. Duke Math. Journal 20: 37-40, 1953.
KATO, T. Perturbation Theory for Linear Operators. Springer-Verlag New York, Inc., 1966.
LABORDE, F. Sur un Probleme Inverse d'un Probleme de Valeurs Propres. C.R. Acad. Sc. París 268: 153-156, 1969.
MIRSKY, L. The Spread of a Matrix. Mathematics 3: 127-130, 1956.
MOREL, P. A Propos d'un Probleme Inverse de Valeurs Propres. C.R. Acad. Sc. París 277: 125-128, 1973.
___. Sur le Probleme Inverse des Valeurs Propes. Numerisehe MathematTk 23: 83-94, 1974.
___. Des Algorithmes pour le Probleme Inverse des Valeurs Propres. Linear Algebra and its Applications 13: 251-273, 1976.
WILKINSON, J.H. The Algebraic Eigenvalue Problem. Oxford University Press, London, 1965.
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2018-04-02
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How to Cite
[1]
“Condiciones para el problema aditivo inverso de autovalor”., Proyecciones (Antofagasta, On line), vol. 8, no. 16, pp. 1–15, Apr. 2018, doi: 10.22199/S07160917.1990.0016.00001.