# The Complete Canonical Piecewise-Linear Representation I. The Geometry of the Domain Space

### C. Kahlert and Leon O. Chua

###
EECS Department

University of California, Berkeley

Technical Report No. UCB/ERL M90/26

1990

Continuous piecewise-linear functions from n m IR to IR are analyzed in terms of the dimension of their domain space and of degenerate k-th order intersections of region boundaries. The theory developed demonstrates how these two quantities are connected. Moreover, the exact number of independent parameters will be demonstrated for boundary configurations containing degenerate intersections of arbitrary orders.

BibTeX citation:

@techreport{Kahlert:M90/26, Author = {Kahlert, C. and Chua, Leon O.}, Title = {The Complete Canonical Piecewise-Linear Representation I. The Geometry of the Domain Space}, Institution = {EECS Department, University of California, Berkeley}, Year = {1990}, URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/1990/1450.html}, Number = {UCB/ERL M90/26}, Abstract = {Continuous piecewise-linear functions from n m IR to IR are analyzed in terms of the dimension of their domain space and of degenerate k-th order intersections of region boundaries. The theory developed demonstrates how these two quantities are connected. Moreover, the exact number of independent parameters will be demonstrated for boundary configurations containing degenerate intersections of arbitrary orders.} }

EndNote citation:

%0 Report %A Kahlert, C. %A Chua, Leon O. %T The Complete Canonical Piecewise-Linear Representation I. The Geometry of the Domain Space %I EECS Department, University of California, Berkeley %D 1990 %@ UCB/ERL M90/26 %U http://www.eecs.berkeley.edu/Pubs/TechRpts/1990/1450.html %F Kahlert:M90/26