Author | Borre, Kai. author |
---|---|
Title | Plane Networks and their Applications [electronic resource] / by Kai Borre |
Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 2001 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-0165-6 |
Descript | XIII, 170 p. online resource |
1 Introduction -- 1.1 Description of the Discrete Model -- 1.2 Description of the Continuous Model -- 1.3 Variance Propagation -- 2 Discrete Approach -- 2.1 Motivation for the Study -- 2.2 Basic Matrix of Leveling -- 2.3 Regular Traverse -- 2.4 Varying the Boundary Conditions -- 2.5 Variance Propagation -- 2.6 Asymptotic Behavior of the Node Variance -- 2.7 On the Smoothness and Roughness of the Eigenvectors -- 2.8 Greenโs Formula for Plane Trigonometric Networks -- 3 Continuous Approach -- 3.1 Leveling Networks -- 3.2 Advanced Error Analysis -- 3.3 Plane Elastic Continuous Networks: A Heuristic Exposition -- 3.4 Distance Networks -- 3.5 Estimates of the Weighted Square Sum of Residuals: the Korn Inequality -- 4 Networks with Relative Observations -- 4.1 Dealing with Relative Observations -- 4.2 Fundamental Solution -- 4.3 Solution of the Boundary Value Problem -- 5 Spectrum -- 5.1 Spectral Density of the Discrete Laplacian -- 5.2 Spectral Distribution Function N(?) -- 5.3 Additional Remarks on the Spectral Properties of Geodetic Networks -- 6 Simple Applications -- 6.1 Stiffness Matrix in Practice -- 6.2 Displacement Functions given a Priori -- 6.3 Merging of Digitized Maps -- 6.4 Interpolation of Discrete Vector Field: Cubic Splines -- Author Index