S-transformations and criterion matrices:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Delft
Rijkscommissie voor Geodesie
1973
|
| Schriftenreihe: | Publications on geodesy
New series ; 5,1 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 168 S. graph. Darst. |
| ISBN: | 9061322189 |
Internformat
MARC
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| 245 | 1 | 0 | |a S-transformations and criterion matrices |c by W. Baarda |
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| 490 | 1 | |a Publications on geodesy : New series |v 5,1 | |
| 650 | 4 | |a Matrices | |
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Datensatz im Suchindex
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|---|---|
| adam_text | CONTENTS
1 An outline of the ideas and their origin 5
An answer to problematical points stated earlier 5
On the origin of the theory of criterion matrices 6
Some algebraic considerations 8
Further speculative considerations 11
The search for a system of interconnected criteria for reliability and precision 12
Introduction to the next sections 13
a Difference equations Elimination of parameters 13
b x, y-coordinate systems used 15
c Outline of the next sections 16
Notes to section 1 18
2 The model of the similarity transformations 20
The case y(°) —1 =(5(a)^0 21
Meaning of dz/”) 22
Remark 23
Note to section 2 Remarks to figures in [5] 24
3 A non-singular S-transformation 30
Note to section 3 An alternative form of the non-singular S-transformation treated 33
4 The connection with earlier ideas 36
Lagrange’s interpolation formula 36
Transition of S-system to (a)-system 37
f*,S
The connection with earlier definitions of S-transformafions 37
The position of the similarity transformation 38
Note to section 4 An intuitive interpretation of S-transfofmations 38
5 Adjustment to given coordinates 40
6 The application of non-singular S-transformations to the adjustment model 44
7 Adjustment to given coordinates without correcting them 46
8 The comparison of a covariance matrix {of coordinates) with a criterion matrix 48
Note to section 8 Change of the form of H(rs 51
9 The comparison of a covariance matrix with a criterion matrix in an adjustment
to given coordinates 53
10 The necessity of S-systems for testing on precision 57
11 The problem of levelling networks treated as an introduction to the construction
of criterion matrices 60
12 Criterion matrices for levelling networks 63
13 Introduction of Jd2-terms in criterion matrices for levelling networks 66
Note to section 13 The positive definiteness of the criterion matrix of the type considered 70
14 The law of propagation of variances for complex coordinate variates Circular
standard ellipses 76
Circular standard ellipses 77
Note to section 14 Conformal mapping 79
15 Criterion matrices in networks for horizontal control 81
Quadrilateral inscribable in a circle 91
Relation with the matrix of the HTW-1956 93
Reference to section 16 96
Note to section 15 Derivation of formulae (15 5) 96
15a Criterion matrices in systems for horizontal control Ad2-terms An alternative
derivation 100
Introduction of Zl 72-terms 107
Parameters of the criterion matrix 109
16 Axiomatic approach to the model of S-systems Ill
Definition Azi(~rs Ill
^-conditions for consistent triangle Ill
R-conditions for consistent quadrangle 113
From quadrangle to pentagon 116
The general S-transformation 119
Extension to R-gon 120
Note to section 16 Conditions in quadrangle and pentagon according to [2] 120
17 Connection of several stochastically independent coordinate systems by means of
S-transformations 124
Computation of corrections to “free” variates 125
Connection of systems (1) and (2) 126
Connection of systems (2) and (3) 127
Connection of systems (3) and (4) 128
Connection of systems (1)—(4) 130
Connection of systems (1)—(4) with system (a) 130
Two or more “given points” in the systems (1)—(4) 132
Given coordinates must not be corrected 133
Adjustment of photogrammetric networks by connecting “independent models” 133
Notes to section 17 135
18 Application of the theory 136
The evolution of ideas 136
Examples 139
Analysis of 2max in free and border partial networks 157
Note 1 to section 18 The factor la2 160
Notes 2-8 to section 18 167
References 168
|
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| id | DE-604.BV005907725 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:36:39Z |
| institution | BVB |
| isbn | 9061322189 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003697827 |
| oclc_num | 3234092 |
| open_access_boolean | |
| owner | DE-91 DE-BY-TUM DE-83 DE-706 |
| owner_facet | DE-91 DE-BY-TUM DE-83 DE-706 |
| physical | 168 S. graph. Darst. |
| psigel | TUB-nveb |
| publishDate | 1973 |
| publishDateSearch | 1973 |
| publishDateSort | 1973 |
| publisher | Rijkscommissie voor Geodesie |
| record_format | marc |
| series | Publications on geodesy |
| series2 | Publications on geodesy : New series |
| spelling | Baarda, Willem Verfasser aut S-transformations and criterion matrices by W. Baarda Delft Rijkscommissie voor Geodesie 1973 168 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Publications on geodesy : New series 5,1 Matrices Transformations (Mathematics) Matrizenrechnung (DE-588)4126963-9 gnd rswk-swf Geodäsie (DE-588)4020202-1 gnd rswk-swf Geodäsie (DE-588)4020202-1 s DE-604 Matrizenrechnung (DE-588)4126963-9 s Publications on geodesy New series ; 5,1 (DE-604)BV001893158 5,1 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003697827&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Baarda, Willem S-transformations and criterion matrices Publications on geodesy Matrices Transformations (Mathematics) Matrizenrechnung (DE-588)4126963-9 gnd Geodäsie (DE-588)4020202-1 gnd |
| subject_GND | (DE-588)4126963-9 (DE-588)4020202-1 |
| title | S-transformations and criterion matrices |
| title_auth | S-transformations and criterion matrices |
| title_exact_search | S-transformations and criterion matrices |
| title_full | S-transformations and criterion matrices by W. Baarda |
| title_fullStr | S-transformations and criterion matrices by W. Baarda |
| title_full_unstemmed | S-transformations and criterion matrices by W. Baarda |
| title_short | S-transformations and criterion matrices |
| title_sort | s transformations and criterion matrices |
| topic | Matrices Transformations (Mathematics) Matrizenrechnung (DE-588)4126963-9 gnd Geodäsie (DE-588)4020202-1 gnd |
| topic_facet | Matrices Transformations (Mathematics) Matrizenrechnung Geodäsie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003697827&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV001893158 |
| work_keys_str_mv | AT baardawillem stransformationsandcriterionmatrices |