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1
Bistatic Radar, Second Edition
4.3 OVALS OF CASSINI The formal definition of an oval of Cassini is the locus of
the vertex of a triangle when the product of the sides adjacent to the vertex is
constant and the length of the opposite side is fixed [137]. When applied to the ...
2
Encyclopaedia
of Mathematics, Supplement III
[7] Varga, R.S., and Krautstengl, A.: 'On Gersgorin-type problems and ovals of
Cassini', Electron. Trans. Numer. Anal. 8 (1999), 15-20. Richard S. Varga
MSC1991: 15A18 Gleason-Kahane-Zelazko theorem - Let F be a non-zero linear
and ...
3
Fundamentals
of Multisite Radar Systems: Multistatic Radars ...
It is the locus of constant product of distances from two given points (foci) [25]
where transmitting and receiving stations are located. In other words, the ovals of
Cassini are contours of constant SNR on any bistatic plane assuming the right
side ...
4
Matrix Iterative Analysis
1.6 As mentioned in the text, the ovals of Cassini, which first appeared in Brauer (
1946), provide an eigenvalue inclusion region for a given nxn matrix A, and, as
mentioned in (1.50) of Theorem 1.24, the union of the Cassini ovals can be no ...
5
Geršgorin and His Circles
Brauer's name had become synonymous with the ovals of Cassini, but, for
unknown reasons, they are rarely mentioned, even though they are superior (cf.
Theorem 2.3) to the Gersgorin disks. (An exception is the book by Korganoff (
1961).) ...
6
Computational Solution
of Nonlinear Systems
of Equations
The ovals of Cassini and the level curves of sin z and cos.:. The regions of
convergence of the iteration functions (1.3) and (1.4) used to solve (1.1) will
involve two families of plane curves, namely, the ovals of Cassini and the level
curves of sin ...
Eugene L. Allgower, Kurt Georg
7
Handbook
of Linear Algebra
(Brauer) Let A = [fl,,] € C"x" and define the quantities Consider the ovals of
Cassini, which are defined by Vi,j = {zeC:|z-fl/,-||z-flj; < RjRj) (i, j = 1,2,. . .,n,i ^ j).
Then all the eigenvalues of A lie in the union of the ovals of Cassini; that is, n o(A)
C |J V,, ...
8
Handbook
of Linear Algebra, Second Edition
(Brauer) Let A I [a,j] G (Cnxn and define the quantities TL i: aij i: , ,... R [ [ ( 12 I1 #1
,n). Consider the ovals of Cassini, which are defined by V7.7 I {Z G C1|z— aii||ZI
an] S RiRj} (M I 1,2,-~inii If) Then all the eigenvalues of A lie in the union of the ...
9
An elementary treatise on plane geometry: according to the ...
To find the equation of the ovals of Cassini. Let AB, the line joining the two given
points (fig. 101) and the perpendicular to it through its point of bisection, be taken
as axes of co-ordinates. Let the given space be — I2, and AB = 2 a, and let P ...
10
Modeling
of Curves and Surfaces with MATLAB®
It was studied by Torricelli in 1645. Its equation is p I a liossilgp, Figure 1.20(a).
hold on; ezpolar('(1 + sin(t))/cos(t)', [-pi/2, pi/2-.5]) ezpolar('(1 + sin(t))/cos(t)', [pi/2+
.5, 3*pi/2]); axis equal 4. The ovals of Cassini are defined to be the sets of points
...
