Abstract
Bounds for the eigenvalues of Ax = λBx are derived where A and B are symmetric and B is also positive definite with a matrix factor G such that B = GTG. The method depends on it being possible to obtain a lower bound for the singular values of G by a method recently developed by the author.
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References
ALAN JENNINGS, Bounds for the singular values of a matrix, IMAJNA, to be published.
A.S. HOUSEHOLDER, The Theory of Matrices in Numerical Analysis, Dover, New York, 1964.
J.H. WILKINSON, The Algebraic Eigenvalue Problem, Oxford, Clarendon Press, 1965.
ALAN JENNINGS, Matrix Computation for Engineering and Scientists, Wiley, London, 1977.
H.G. ALLEN, and P.S. BULSON, Background to Buckling, McGraw-Hill, London, 1980.
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© 1983 Springer-Verlag
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Jennings, A. (1983). On bounds for symmetric eigenvalue problems. In: Kågström, B., Ruhe, A. (eds) Matrix Pencils. Lecture Notes in Mathematics, vol 973. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062103
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DOI: https://doi.org/10.1007/BFb0062103
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