Skip to main content
SpringerLink
Log in

Ladder networks, fixpoints, and the geometric mean

  • Published:
Circuits, Systems and Signal Processing Aims and scope Submit manuscript

Abstract

Using fixed-point arguments, existence and uniqueness results are obtained for the joint resistance of infinite positive operator networks with noncommuting operators in the branches. Explicit representations for the joint resistance are given using the geometric mean of positive operators.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Anderson, W. N. Jr., Shorted Operators, SIAM J. Appl. Math.20 (1971), 520–525.

    Google Scholar 

  2. Anderson, W. N. Jr. and R. J. Duffin, Series and Parallel Addition of Matrices, J. Math. Anal. Appl.26 (1969), 576–594.

    Google Scholar 

  3. Anderson, W. N. Jr. and G. Trapp, Shorted Operators II, SIAM J. Appl. Math.28 (1975), 160–171.

    Google Scholar 

  4. Anderson, W. N. Jr. and G. Trapp, Operator Means and Electrical Networks, Proc. 1980 IEEE International Symposium on Circuits and Systems (1980), 523–527.

  5. Ando, T., Topics on Operator Inequalities, Lecture Note. Hokkaido University, Sapporo, 1978.

    Google Scholar 

  6. Ando, T., Fixed Points of Certain Maps on Positive Semidefinite Operators, Lecture Note. Hokkaido University, Sapporo, 1980.

    Google Scholar 

  7. Fair, W., Noncommutative Continued Fractions, SIAM J. Math. Anal.2 (1971), 226–232.

    Google Scholar 

  8. Hanna, M. P., Generalized Overrelaxation and Gauss-Seidel Convergence on Hilbert Space, Proc. AMS35 (1972), 524–530.

    Google Scholar 

  9. Krein, M.G., The Theory of Selfadjoint Extensions of Semibounded Hermitian Operators and its Applications, Mat. Sb.20 (1947), 431–495.

    Google Scholar 

  10. Pusz, W. and S. L. Woronowicz, Functional Calculus for Sesquilinear Forms and the Purification Map, Rep. Math. Phys.8 (1975), 159–170.

    Google Scholar 

  11. Zemanian, A. H., Infinite Electrical Networks, Proc. IEEE64 (1976), 6–17.

    Google Scholar 

  12. Zemanian, A. H., Characteristic — Resistance Method for Grounded Semi-Infinite Grids, SIAM J. Math. Anal.12 (1981), 115–138.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, East Tennessee State University, 37614, Johnson City, TN

    W. N. Anderson Jr.

  2. School of Mathematics, Georgia Institute of Technology, 30332, Atlanta, GA

    T. D. Morley

  3. Department of Statistics and Computer Science, West Virginia University, 26506, Morgantown, WV

    G. E. Trapp

Authors
  1. W. N. Anderson Jr.
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. D. Morley
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. G. E. Trapp
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This research was supported by the National Science Foundation under Grant MCS 80-01906.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Anderson, W.N., Morley, T.D. & Trapp, G.E. Ladder networks, fixpoints, and the geometric mean. Circuits Systems and Signal Process 2, 259–268 (1983). https://doi.org/10.1007/BF01599069

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01599069

Keywords

Search

Navigation