zbMATH — the first resource for mathematics

L’addition parallèle d’opérateurs interprétée comme inf- convolution de formes quadratiques convexes. (French) Zbl 0599.94010
Given two parallel circuits with resistance determined by semi-definite positive matrices A, B, the equivalent resistance of the circuits is expressed in terms of A and B by the so-called parallel sum of the operators A and B. We interpret this operation as the inf-convolution of the quadratic forms associated to A and B. The properties of the parallel sum are then deduced from those of the inf-convolution of convex functions.

94C05 Analytic circuit theory
15A63 Quadratic and bilinear forms, inner products
Full Text: DOI EuDML
[1] W. N. ANDERSON Jr., Shorted Operators, SIAM J. AppL Math., 20 (1971) pp. 520-525. Zbl0217.05503 MR287970 · Zbl 0217.05503 · doi:10.1137/0120053
[2] W. N. ANDERSON Jr. and R. J. DUFFIN, Series and parallel addition of matrices, J. Math. Anal. Appl., 26 (1969) pp. 576-594. Zbl0177.04904 MR242573 · Zbl 0177.04904 · doi:10.1016/0022-247X(69)90200-5
[3] W. N. ANDERSON Jr. and M. SHREIBER, On the infimum of two projections, Acta Sci Math. (Szeged), 33 (1972) pp. 165-168. Zbl0258.46023 MR322486 · Zbl 0258.46023
[4] W. N. ANDERSON Jr. and G. E. TRAPP, Inequalities for the parallel connection of resistive n. port networks, J. Franklin Inst., 5 (1975) pp. 305-313. Zbl0349.94044 MR429347 · Zbl 0349.94044 · doi:10.1016/0016-0032(75)90169-6
[5] W. N. ANDERSON Jr. and G. TRAPP, Shorted Operators, SIAM J. Appl. Math., 28 (1975) pp. 60-71. Zbl0295.47032 MR356949 · Zbl 0295.47032 · doi:10.1137/0128007
[6] P. J. LAURENT, Approximation et Optimisation, Hermann (1972). Zbl0238.90058 MR467080 · Zbl 0238.90058
[7] J. J. MOREAU, Fonctionnelles convexes, séminaire sur les équations aux dérivées partielles II, Collège de France (1966-1967). MR390443
[8] R. T. ROCKAFELLAR, Convex Analysis, Princeton University Press (1970). Zbl0193.18401 MR274683 · Zbl 0193.18401
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.