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Plane networks and their applications

Author: K Borre
Publisher: Boston : Birkhäuser, ©2001.
Edition/Format:   Book : EnglishView all editions and formats
Database:WorldCat
Summary:
"This text introduces the concepts and applications behind plane networks. Currently, there is nothing in book form dealing with the topics covered in this work. The presentation unfolds in a systematic, user-friendly style and goes from the basics to cutting-edge research." "Key features include: presentation of the basics required - fundamental material from linear algebra and differential equations; examination  Read more...
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Additional Physical Format: Online version:
Borre, K. (Kai).
Plane networks and their applications.
Boston : Birkhäuser, ©2001
(OCoLC)700090165
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: K Borre
ISBN: 0817641939 9780817641931 3764341939 9783764341930
OCLC Number: 45093787
Description: x, 170 pages : illustrations ; 24 cm
Contents: 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.
Responsibility: Kai Borre.
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Abstract:

Introduces the concepts and applications behind plane networks. This book presents fundamental material from linear algebra and differential equations, and offers several different applications of  Read more...

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"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 Read more...

 
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schema:reviewBody""This text introduces the concepts and applications behind plane networks. Currently, there is nothing in book form dealing with the topics covered in this work. The presentation unfolds in a systematic, user-friendly style and goes from the basics to cutting-edge research." "Key features include: presentation of the basics required - fundamental material from linear algebra and differential equations; examination of classical mathematical tools for analyzing discrete networks, followed by a well-developed theory, which is the continuous analogue of a discrete network; transition from the discrete to the continuous case, described via finite elements; Ch. 3 involves an analysis of linear operators, variational calculus, boundary value problems for PDEs, and Green's functions; Green's functions are the continuous analogue of the discrete error covariance functions, and form the basis for all types of error prediction; techniques applied to leveling and other observation types of networks in one and two dimensions; several different applications of the continuous theory; practical problems, supported by MATLAB files, underscore the continuous theory; and bibliography of recent results and index." "Plane Networks and their Applications is aimed at applied mathematicians, mechanical engineers, geodesists and graduate students, and should be an excellent text for self-study, classroom, or reference use."--Jacket."
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