Plane Networks and Their Applications

ISBN-13: 9781461266426 / Angielski / Miękka / 2012 / 170 str.

Kai Borre

Opis

This concise, fast-paced text introduces the concepts and applications behind plane networks. It presents fundamental material from linear algebra and differential equations, and offers several different applications of the continuous theory. Practical problems, supported by MATLAB files, underscore the theory; additional material can be downloaded from the author's website.

Recenzje

"This concise book renders an advanced exposition of the theory of error propagation in geodetic networks that are comprised of up to a few hundred nodes... The reviewed book constitutes a timely and valuable contribution to the theory of plane geodetic network analysis and design. An outstanding feature of this book is the extensive use it makes of the nowadays easy availability of sophisticated automatic computing tools."  

- Mathematical Reviews

Spis treści

1 Introduction.- 1.1 Description of the Discrete Model.- 1.1.1 Free-Free Network.- 1.1.2 Fixed-Free Network.- 1.1.3 Fixed-Fixed Network.- 1.2 Description of the Continuous Model.- 1.2.1 A to AT: Integration by Parts.- 1.2.2 Green’s Function.- 1.2.3 Change of Boundary Conditions.- 1.2.4 Modified Green Function.- 1.2.5 Green’s Function as a Formal Covariance Function.- 1.3 Variance Propagation.- 2 Discrete Approach.- 2.1 Motivation for the Study.- 2.2 Basic Matrix of Leveling.- 2.2.1 Eigenvectors and Eigenvalues.- 2.2.2 Pseudoinverse.- 2.2.3 Singular Value Decomposition.- 2.2.4 Two-Dimensional Networks.- 2.3 Regular Traverse.- 2.3.1 Random Errors in the Regular Traverse.- 2.3.2 Systematic Errors in the Regular Traverse.- 2.4 Varying the Boundary Conditions.- 2.4.1 Straight Line.- 2.4.2 Circumference of a Circle.- 2.5 Variance Propagation.- 2.6 Asymptotic Behavior of the Node Variance.- 2.7 On the Smoothness and Roughness of the Eigenvectors.- 2.8 Green’s Formula for Plane Trigonometric Networks.- 3 Continuous Approach.- 3.1 Leveling Networks.- 3.1.1 Single Triangle.- 3.1.2 Entire Network.- 3.2 Advanced Error Analysis.- 3.2.1 Green’s Function for the Unit Circle.- 3.2.2 Green’s Function for the Ellipse.- 3.2.3 Green’s Function for the Annulus.- 3.3 Plane Elastic Continuous Networks: A Heuristic Exposition.- 3.4 Distance Networks.- 3.4.1 Single Triangle.- 3.4.2 Distance Network.- 3.4.3 Azimuth Networks.- 3.4.4 Combined Distance and Azimuth 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.