On the additive inverse eigenvalue problem

• Rojo Jeraldo, Óscar Luis ^[1] ; Soto Montero, Ricardo Lorenzo ^[1]
  1. [1] Universidad Católica del Norte

     Universidad Católica del Norte

     Antofagasta, Chile

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 7, Nº. 14, 1988, págs. 1-27
• Idioma: inglés
• DOI: 10.22199/S07160917.1988.0014.00001
• Enlaces
  • Texto completo
• Resumen

  • The problem of determining the eigenvalues of a given matrix A is one of long-standing and wide application in many areas of science and engineering. By contrast, the problem of determining all or some of the entries of A fron spectral information is a new subject which has only recently become an active area of research. We quote Z. Bohte [2], (p. 385, 1967): "For the numerical solution of this problem a number of techniques have been used without sufficient theoretical consideration. We believe the problem has not attracted the attention of the mathematicians yet".

• Referencias bibliográficas
  • Citas 1. Biegler-Konig, F. W. Sufficient Conditiors for the Solvability of Inverse Eigenvalue Problems. Linear Algebra and Its Applications...
  • Bohte, Z. Numerical Solution of the Inverse Algebraic Eigenvalue Problem. Computer Journal 10: 385-388, 1967/1968.
  • Brussard, P. J., and Glaudemans, P. W. Shell Model Applications in Nuclear Spectroscopy. Elsevier, New York, 1977.
  • De Oliveira, G. N. Note on an Inverse Characteristic Value Problem. Numerische Mathematik 15: 345-347, 1970.
  • Downing, A. C., Jr., and Householder, A. S. Some Inverse Characteristic Value Problems. Journal Assoc. for Computing Machinery 3: 203-207,...
  • Faddeyev, L. D. The Inverse Problem in the Quantun Theory of Scattering. Journal of Mathematical Physics 4: 72-104, 1963.
  • Fletcher, R. Semi-definite Matrix Constraints in Optimization. Siam Journal Control Optimization 23: 493-513, 1985.
  • Friedland, S. lnverse Eigenvalue Problems. Linear Algebra and lts Applications 17: 15-51, 1977.
  • Friedland, S., Nocedal, J., and Overton, M. L. The Formulation and Analysis of Numerical Methods for lnverse Eigenvalue Problems. Siam Journal...
  • Hadeler, K. P. Ein Inverses Eigenwertproblem. Linear Algebra and Its Applications 1: 83-101, 1968.
  • Hoffman, A., and Wielandt, H. The Variation of the Spectrum of a Normal Matrix. Duke Math. Journal 2O: 37 - 4O, 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. Paris 268: 153-156, 1969.
  • Marcus, M, and Mino, H. A Survey of Matrix Theory and Matrix Inequalities. Allyn and Bacor, Boston, 1964.
  • 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. Paris 277: 125-128, 1973.
  • . Morel, P . Sur le Probleme Inverse des Valeurs Propres. Numerische Mathematik 23: 83-94, 1974.
  • Morel, P. Des Algorithmes pour le Probleme Inverse des Valeurs Propres. Linear Algebra and Its Applications 13: 251-273, 1976.
  • Pliva, J., and Toman, S. Multiplicity of Solutions of the lnverse Secular Problem. Journal of Molecular Spectroscopy 21: 362-371, 1966.
  • Soto, R. L. On Matrix Inverse Eigenvalue Problems. Ph. D. Dissertation. New Mexico State University, 1987.
  • Stewart, G. W. Introduction to Matrix Computation. Academic Press, New York, 1973.
  • Wilkinson, J. H. The Algebraic Eigenvalue Problem. Oxford University Press, London, 1965.