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Circumscribing an Ellipsoid about the Intersection of Two Ellipsoids

Published online by Cambridge University Press:  20 November 2018

W. Kahan
W. Kahan*
Affiliation:
University of Toronto
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An ellipsoid G is associated uniquely with a positive definite matrix A via

Note that all ellipsoids discussed here are centred at 0. Given G1, and G2 we seek another ellipsoid circumscribed about G1 ∩ G2. It is easy to see that

if and only if x'hx ≤ maxi x'aix for all vectors x.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 11 , Issue 3 , August 1968 , pp. 437 - 441
Copyright
Copyright © Canadian Mathematical Society 1968

References

Burrows, J. W. (1966), Maximization of a second-degree polynomial on the unit sphere. Math, of Comp. 20, 441-444.Google Scholar
Forsythe, G.E. and Golub, G. H. (1965), On the stationary values of a second-degree polynomial on the unit sphere. J. Soc. Indust. Appl. Math. 13, 1050-1068.Google Scholar
Kahan, W. (1967), Circumscribing an ellipsoid about the Minkowski sum of given ellipsoids. (Submitted to J. Linear Algebra). *Google Scholar
Kahan, W. (1968), An ellipsoidal error bound for linear systems of ordinary differential equations. (Manuscript to appear).Google Scholar
Schweppe, F. C. (1967), Recursive state estimation when observation errors and system inputs are bounded. (Sperry Rand Research Centre Report RR-67–25, Sudbury, Mass.)Google Scholar