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Some Modified Matrix Eigenvalue Problems

Gene H. Golub
SIAM Review
Vol. 15, No. 2, Part 1 (Apr., 1973), pp. 318-334
Stable URL: http://www.jstor.org/stable/2028604
Page Count: 17
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Some Modified Matrix Eigenvalue Problems
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Abstract

We consider the numerical calculation of several matrix eigenvalue problems which require some manipulation before the standard algorithms may be used. This includes finding the stationary values of a quadratic form subject to linear constraints and determining the eigenvalues of a matrix which is modified by a matrix of rank one. We also consider several inverse eigenvalue problems. This includes the problem of determining the coefficients for the Gauss-Radau and Gauss-Lobatto quadrature rules. In addition, we study several eigenvalue problems which arise in least squares.

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