Continuous Networks I

Summary

Criterion matrices/ideal variance — covariance matrices are constructed from continuous networks being observed by signal derivatives of first and second order. The method of constrained least- squares leads to differential equations up to fourth order, to characteristic boundary values and constraints according to the datum choice. Here only onedimensional networks on a line and on a circle are discussed. Their characteristic (modified) Green function is constructed and used for the computation of the variance — covariance function of adjusted mean signal functions. Finally numerical aspects originating fm the discrete nature of real observational series are discussed. In detail, the transformation of a criterion matrix into a network datum and its comparison with the variance — covariance matrix of an ideally configurated network is presented.