A Global Representation of Multidimensional Piecewise-Linear Functions with Linear Partitions

IEEE Transactions on Circuits and Systems

Volumn CAS-25, Issue 11, 1978, Pages 938-940

  Kang, S M ^a,b   Chua, Leon O ^c  

^a RUTGERS UNIVERSITY   (United States)

^b LUCENT TECHNOLOGIES   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL TECHNIQUES - PIECEWISE LINEAR TECHNIQUES;

ELECTRIC NETWORKS;

EID: 0018035219     PISSN: 00984094     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCS.1978.1084401     Document Type: Article

References (11)

1. L. O. Chua, Introduction to Nonlinear Network Theory. New York: McGraw-Hill, 1969.
2. —, “Modeling of three-terminal devices: A black-box approach,” IEEE Trans. Circuit Theory, vol. CT-19, pp. 555–562, Nov. 1972.
3. L. O. Chua and P. -M. Lin, Computer-Aided Analysis of Electronic Circuits: Algorithms and Computational Techniques. Englewood Cliffs,. NJ: Prentice-Hall, 1975.
4. J. Katzenelson, “An algorithm for solving nonlinear resistive networks,” Bell Syst. Tech. J., vol. 44, pp. 1605–1620, 1965.
5. T. Fujisawa, E. S. Kuh, and T. Ohtsuki, “A sparse matrix method for analysis of piecewise-linear networks,” IEEE Trans. Circuit Theory, vol. CT-19, pp. 571–584, Nov. 1973.
6. M. -J. Chien and E. S. Kuh, “Solving piecewise-linear equations for resistive networks,” Int. J. Circuit Theory Applications, vol. 4, no. 1, pp. 3–24, Jan. 1976.
7. T. Ohtsuki, T. Fujisawa, and S. Kumagai, “Existence theorems and a solution algorithm for piecewise-linear resistor networks,” SIAM J. Math. Anal., vol. 8, no. 1, Feb. 1977.
8. M. -J. Chien and E. S. Kuh, “Solving nonlinear resistive networks using piecewise-linear analysis and simplicial subdivision,” IEEE Trans. Circuits and Systems, CAS-24, pp. 305–317, June 1977.
9. L. O. Chua and S. M. Kang, “Section-wise piecewise-linear functions: Canonical representation, properties, and applications,” Proc. IEEE, (Special Issue on Multidimensional Systems), vol. 65, pp. 915–929, June 1977.
10. P. B. Zwart, “Multivariate splines with nondegenerate partitions,” SIAM J. Numer. Anal., vol. 10, no. 4, pp. 665–673, Sept. 1973.
11. T. Fujisawa and E. S. Kuh, “Piecewise-linear theory of nonlinear networks,” SIAM J. Appl. Math., vol. 22, no. 2, pp. 307–328, Mar. 1972.