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Existence for a matrix equation arising in microelectronics
Author(s):
Jonq
Juang
Journal:
Proc. Amer. Math. Soc.
124
(1996),
3477-3480.
MSC (1991):
Primary 78A25, 15A24
MathSciNet review:
1343703
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Abstract:
In this paper we rigorously show the existence of solutions of a matrix equation which arises in the design of micro electronical circuits. This equation was studied by Szidarovszky and Palusinsk [Appl. Math. Comput. 64, 115-119(1994)], who also presented an iterative algorithm for its solution. We show, via an example, that this algorithm could converge extremely slow in certian cases. The solution can then be used to minimize the reflection coefficients of the active signals.
References:
- 1.
- C. S. Chang, Electrical design of signal lines for multilayer printed circuit boards, IBM J. Res. Dev. 32(1988) 647-657.
- 2.
- F. Szidarovszky and O. A. Palusinski, A special matrix equation and its application in microelectronics, Appl. Math. Comput. 64(1994) 115-119. MR 95e:94065
- 3.
- J. M. Ortega and W. C. Rheinboldt, Iterative solution of nonlinear equations in several variables, Academic Press, New York, 1970. MR 42:8686
- 4.
- V. Hutson and J. S. Pym, Applications of functional analysis and operator theory, Academic Press, New York, 1980. MR 81i:46001
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Additional Information:
Jonq
Juang
Affiliation:
Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan, Republic of China
Email:
jjuang@math.nctu.edu.tw
DOI:
10.1090/S0002-9939-96-03499-5
PII:
S 0002-9939(96)03499-5
Keywords:
Microelectronics,
$M$-matrix,
a priori bounds,
degree theory
Received by editor(s):
March 10, 1995
Received by editor(s) in revised form:
May 22, 1995
Additional Notes:
The work is partially supported by the National Science Council of Taiwan, R. O. C
Communicated by:
David H. Sharp
Copyright of article:
Copyright
1996,
American Mathematical Society
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