Existence for a matrix equation arising in microelectronics

Juang, Jonq

doi:10.1090/S0002-9939-96-03499-5

Existence for a matrix equation arising in microelectronics
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Proc. Amer. Math. Soc. 124 (1996), 3477-3480 Request permission

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

C. S. Chang, Electrical design of signal lines for multilayer printed circuit boards, IBM J. Res. Dev. 32(1988) 647-657.
Ferenc Szidarovszky and Olgierd A. Palusinski, A special matrix equation and its application in microelectronics, Appl. Math. Comput. 64 (1994), no. 2-3, 115–119. MR 1298256, DOI 10.1016/0096-3003(94)90057-4
J. M. Ortega and W. C. Rheinboldt, Iterative solution of nonlinear equations in several variables, Academic Press, New York-London, 1970. MR 0273810
V. Hutson and J. S. Pym, Applications of functional analysis and operator theory, Mathematics in Science and Engineering, vol. 146, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1980. MR 569354, DOI 10.1016/S0076-5392(08)62876-3