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| Title: | Mathematics at DEC |
|
| Moderator: | RUSURE::EDP |
|
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
1966.0. "A Problem on Lipschitz Continuity" by PASTA::SUDHARSANAN () Tue Apr 18 1995 18:37
Let M be an n by n real matrix, x be an n-length column vector, and
a(x) be a vector with each element a_i(x_i) - a bounded, strictly
monotonic, C-infinity function. Consider the following equations
x = M a(x) + c
y = u'x
where c and u are n-length column vectors and y is a scalar.
Allow the elements of M to be a vector mu of length n times n.
When is the partial derivative of y with respect to mu
Lipschitz on mu? Are there particular matrix properties that M
has to satisfy for this?
The above equations arise in some circuit problems as described
by A.N. Wilson, Nonlinear Networks: Theory and Analysis. The
specific problem occurs when certain circuit parameters are to
be changed to obtain desirable performance.
S. Sudharsanan
[email protected]
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