ovals of Cassini


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Related to ovals of Cassini: nephroid of Freeth

ovals of Cassini

pl n
(Mathematics) maths the locus of a point x, whose distance from two fixed points, a and b, is such that |xa| |xb| is a constant
[C18: named after G. D. Cassini]
References in periodicals archive ?
Here, we investigate the relationships between G(A), the union of Gersgorin disks, K(A), the union of Brauer ovals of Cassini, and B(A), the union of Brualdi lemniscate sets, for eigenvalue inclusions of an n x n complex matrix A.
Gersgorin disks, Brauer ovals of Cassini, Brualdi lemniscate sets, minimal Gersgorin sets.
In other words, for n [greater than or equal to] 3, each point of the Brauer ovals of Cassini K(A) is an eigenvalue of some matrix in (A) or [?
1) are lemniscates of order 1, while the Brauer ovals of Cassini [K.
8) requires more information from the matrix A, in order to form the Brualdi lemniscate set B(A), then is required by the Brauer ovals of Cassini K(A) or the Gersgorin disks G(A), one might expect that B(A) is a set, which is no larger, in the complex plane, than K(A) or G(A).
Comparison of Brauer's Ovals of Cassini and Brualdi's Lemniscate Sets.
This establishes that the Brualdi lemniscate set for a matrix A is always no larger than the union of the Brauer ovals of Cassini for this matrix.
In other words, the Brualdi lemniscate set B(A) need not, in general, be a proper subset of the Brauer ovals of Cassini K(A).
VARGA, Gerschgorin disks, Brauer ovals of Cassini (a vindication), and Brualdi sets, Information (to appear).