Fitting linear relationships: a history of the calculus of observations ; 1750 - 1900
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York ; Berlin ; Heidelberg ; Barcelona ; Budapest u.a.
Springer
1999
|
| Schriftenreihe: | Springer series in statistics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 243 - 262 |
| Beschreibung: | XI, 271 S. graph. Darst. |
| ISBN: | 0387985980 |
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Datensatz im Suchindex
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|---|---|
| adam_text | RICHARD WILLIAM FAREBROTHER FITTING LINEAR RELATIONSHIPS A HISTORY OF
THE CALCULUS OF OBSERVATIONS 1750-1900 SPRINGER CONTENTS PREFACE V LIST
OF TABLES XII LIST OF FIGURES XUE CHAPTER 1 INTRODUCTION 1 1.1 THE LINEAR
ESTIMATION PROBLEM 1 1.2 ALGEBRAIC ESTIMATION PROCEDURES 2 1.3 PERIODOF
STUDY 3 1.4 LINEAR ALGEBRA AND LINEAR PROGRAMMING 4 1.5 TERMINOLOGY 5
1.6 NOTATION , 6 UCITATION 7 CHAPTER 2 THE METHODS OF BOSCOVICH AND
MAYER 9 2.1 HISTORICAL BACKGROUND AND THE LIFE OF MAYER 9 2.2 THE
LONGITUDE PROBLEM 11 2.3 MAYER S METHOD 11 2.4 MERIDIAN ARE MEASUREMENTS
15 2.5 THE LIFE OF BOSCOVICH 16 2.6 BOSCOVICH S METHOD 17 2.7
BOSCOVICH S GEOMETRICAL SOLUTION 19 2.8 DISCUSSION 21 2.9 SUMMARY 22
CHAPTER 3 LAPLACE S WORK ON THE METHODS OF BOSCOVICH AND MAYER 23 3.1
HISTORICAL BACKGROUND 23 3.2 THE LIFE OF LAPLACE 24 3.3 LAPLACE S FIRST
VARIANT OF BOSCOVICH S METHOD 25 CONTENTS 3.4 LAPLACE S SECOND VARIANT
OF BOSCOVICH S METHOD 27 3.5 LAPLACE S FIRST VARIANT OF THE METHOD OF
AVERAGES 29 3.6 SUMMARY 31 CHAPTER 4 LAPLACE S MINIMAX PROCEDURE 33 4.1
LAPLACE S FIRST SOLUTION 33 4.2 LAPLACE S SECOND SOLUTION 35 4.3
APPLICATIONS 37 4.4 LAPLACE S THIRD SOLUTION AND CAUCHY S GENERALISATION
38 4.5 LATER WORK ON LAPLACE S FIRST SOLUTION 41 4.6 DE PRONY S
GEOMETRICAL SOLUTION 44 4.7 LINEAR PROGRAMMING TECHNIQUES 46 4.8 SUMMARY
47 CHAPTER 5 THE METHOD OF LEAST SQUARES 49 5.1 HISTORICAL BACKGROUND 49
5.2 THE LIFE OF LEGENDRE 49 5.3 LEGENDRE S DERIVATION OF THE METHOD OF
LEAST SQUARES 50 5.4 COTES S RULE AND SIMPSON S PROBLEM 52 5.5 THE LEAST
SUM OF EVEN POWERS 53 5.6 MECHANICAL REPRESENTATIONS 54 5.7 LAPLACE S
HISTORICAL NOTES 59 5.8 LEAST SUM OF ABSOLUTE DEVIATIONS 60 5.9
LAPLACE S ILLUSTRATIVE EXAMPLE 61 5.10 LEGENDRE S ILLUSTRATIVE EXAMPLE
64 5.11 SUMMARY 67 CHAPTER 6 STATISTICAL FOUNDATIONS OF THE METHOD OF
LEAST SQUARES 69 6.1 LAPLACE S REAWAKENING 69 6.2 FITTING CRITERIA 69
6.3 LAPLACE S ILLUSTRATIVE EXAMPLE 72 6.4 BERNOULLI S FITTING PROCEDURE
75 6.5 GAUSS S DERIVATION OF THE NORMAL LAW 77 6.6 SUMMARY 81 CHAPTER 7
ADRAIN S WORK ON THE NORMAL LAW 83 7.1 THE LIFE OF ADRAIN 7.2 BOWDITCH S
METHOD OF CORRECTING A SURVEY 83 84 CONTENTS IX 7.3 ADRAIN S DERIVATION
OF THE NORMAL LAW 85 7.4 APPLICATIONS OF THE NORMAL LAW 86 7.5 PRIORITY
DISPUTES 89 7.6 SUMMARY 90 CHAPTER 8 GAUSS S MOST PROBABLE VALUES 91 8.1
THE LIFE OF GAUSS 91 8.2 MOST PROBABLE VALUES 91 8.3 A MEASURE OF
PRECISION I 94 8.4 A MEASURE OF PRECISION II 97 8.5 EXAMPLE 98 8.6
GAUSS S FORMAL ELIMINATION PROCEDURE 100 8.7 SUMMARY 103 APPENDIX:
GAUSS S MATRIX NOTATION 104 CHAPTER 9 LAPLACE S MOST ADVANTAGEOUS METHOD
105 9.1 THREE LIMIT DISTRIBUTIONS 105 9.2 THE MOST ADVANTAGEOUS VALUES I
107 9.3 THE MOST ADVANTAGEOUS VALUES II 111 9.4 THE PROBABLE ERROR 117
9.5 ADJUSTMENT OF A SIMPLE TRIANGULATION 123 9.6 LAPLACE S LATER
VARIANTS OF THE METHOD OF AVERAGES 125 9.7 THE METHOD OF SITUATION 127
9.8 SUMMARY 130 CHAPTER 10 GAUSS S MOST PLAUSIBLE VALUES 131 10.1 THE
MOST PLAUSIBLE VALUE CRITERION 131 10.2 THE MOST PLAUSIBLE VALUE OF THE
MEAN SQUARED ERROR 133 10.3 THE MOST PLAUSIBLE VALUES OF THE UNKNOWN
CONSTANTS 134 10.4 GAUSS S COMPUTATIONAL PROCEDURE 140 10.5 GAUSS S
UPDATING FORMULAS 144 10.6 CHANGING WEIGHTS 146 10.7 AN APPROPRIATE
VALUE FOR THE MEAN SQUARED ERROR OF INDIRECT OBSERVATIONS 148 10.8
SUMMARY 149 CHAPTER 11 GAUSS S METHOD OF ADJUSTMENT BY CORRELATES 151
11.1 MOST PLAUSIBLE CONSTRAINED VALUES 151 11.2 CONSTRAINED LEAST
SQUARES 157 11.3 INCOMPLETE ADJUSTMENT 159 11.4 THE INVERSE OF A
SYMMETRIE MATRIX 160 CONTENTS 11.5 ORIGINS OF MATRIX THEORY 162 11.6
SUMMARY 162 CHAPTER 12 MECHANICAL ANALOGIES FOR THE METHOD OF LEAST
SQUARES 163 12.1 THE LIFE OF DONKIN 163 12.2 DONKIN S MECHANICAL ANALOGY
163 12.3 NEWCOMB S GEOMETRICAL INTERPRETATIONS OF THE MECHANICAL MODEL
168 12.4 DIRECT DETERMINATION OF THE ERRORS 171 12.5 THE LATENT ROOT
DECOMPOSITION 174 12.6 BRAVAIS S DISTRIBUTIONAL RESULTS 179 12.7
PERPENDICULAR LEAST SQUARES 184 12.8 SUMMARY 188 CHAPTER 13
ORTHOGONALISATION PROCEDURES 191 13.1 LAPLACE S ORTHOGONALISATION
PROCEDURE 191 13.2 THE LIFE OF CAUCHY 196 13.3 CAUCHY S METHOD OF
INTERPOLATION 197 13.4 LATER ORTHOGONALISATION PROCEDURES 202 13.5
CAUCHY S STATISTICAL ARGUMENTS 204 13.6 SUMMARY 205 CHAPTER 14 THIELE S
DERIVATION OF THE METHOD OF LEAST SQUARES 207 14.1 THE LIFE OF THIELE
207 14.2 BOUND AND FREE FUNCTIONS 207 14.3 CANONICAL ADJUSTMENTS 208
14.4 ADJUSTMENT BY CORRELATES 209 14.5 ADJUSTMENT BY ELEMENTS 211 14.6
THE METHOD OF NORMAL PLACES 214 14.7 SUMMARY 216 CHAPTER 15 LATER WORK
ON THE METHOD OF SITUATION 217 15.1 THE LIFE OF EDGEWORTH 217 15.2
EDGEWORTH S FIRST METHOD 218 15.3 TUMER S GRAPHICAL SOLUTION 218 15.4
EDGEWORTH S SECOND METHOD 221 15.5 EDGEWORTH S GEOMETRICAL ANALOGY 224
15.6 EDGEWORTH S DOUBLE MEDIAN METHOD 225 15.7 BOWLEY S VARIANT OF THE
DOUBLE MEDIAN METHOD 227 15.8 RHODES S ALGORITHM 227 CONTENTS XI 15.9
LINEAR PROGRAMMING TECHNIQUES 230 15.10 SUMMARY 231 CHAPTER 16
CONCLUDING REMARKS 233 16.1 NONLINEAR CURVE FITTING PROBLEMS 233 16.2
THE TRUE METHOD OF LEAST SQUARES 235 16.3 CBMPUTATIONAL DIFFICULTIES IN
THE LINEAR CASE 236 16.4 THE SIMULTANEOUS EQUATIONS MODEL 237 16.5
LINEAR REGRESSION ANALYSIS 238 16.6 VANATIONS IN THE LEVEL OF SCIENTIFIC
ACTIVITY 238 16.7 CONTRIBUTIONS TO MATRIX THEORY 239 BIBLIOGRAPHY 243
NAME INDEX 263 SUBJECT INDEX 267
|
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| indexdate | 2024-07-09T18:27:05Z |
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| isbn | 0387985980 |
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| spelling | Farebrother, Richard William 1946- Verfasser (DE-588)12497841X aut Fitting linear relationships a history of the calculus of observations ; 1750 - 1900 Richard William Farebrother New York ; Berlin ; Heidelberg ; Barcelona ; Budapest u.a. Springer 1999 XI, 271 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer series in statistics Literaturverz. S. 243 - 262 Geschichte 1750-1900 gnd rswk-swf Ajustement relation linéaire Estatística (história) larpcal Histoire calcul observation Lineaire analyse gtt Modelos lineares larpcal Moindres carrés ram Méthode Laplace Méthode ajustement Gauss Pesquisa e planejamento estatístico larpcal Regressieanalyse gtt Statistique mathématique - Histoire Statistique mathématique - Histoire ram Tijdreeksen gtt Geschichte Mathematical statistics History Statistik (DE-588)4056995-0 gnd rswk-swf Statistik (DE-588)4056995-0 s Geschichte 1750-1900 z DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008418593&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Farebrother, Richard William 1946- Fitting linear relationships a history of the calculus of observations ; 1750 - 1900 Ajustement relation linéaire Estatística (história) larpcal Histoire calcul observation Lineaire analyse gtt Modelos lineares larpcal Moindres carrés ram Méthode Laplace Méthode ajustement Gauss Pesquisa e planejamento estatístico larpcal Regressieanalyse gtt Statistique mathématique - Histoire Statistique mathématique - Histoire ram Tijdreeksen gtt Geschichte Mathematical statistics History Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4056995-0 |
| title | Fitting linear relationships a history of the calculus of observations ; 1750 - 1900 |
| title_auth | Fitting linear relationships a history of the calculus of observations ; 1750 - 1900 |
| title_exact_search | Fitting linear relationships a history of the calculus of observations ; 1750 - 1900 |
| title_full | Fitting linear relationships a history of the calculus of observations ; 1750 - 1900 Richard William Farebrother |
| title_fullStr | Fitting linear relationships a history of the calculus of observations ; 1750 - 1900 Richard William Farebrother |
| title_full_unstemmed | Fitting linear relationships a history of the calculus of observations ; 1750 - 1900 Richard William Farebrother |
| title_short | Fitting linear relationships |
| title_sort | fitting linear relationships a history of the calculus of observations 1750 1900 |
| title_sub | a history of the calculus of observations ; 1750 - 1900 |
| topic | Ajustement relation linéaire Estatística (história) larpcal Histoire calcul observation Lineaire analyse gtt Modelos lineares larpcal Moindres carrés ram Méthode Laplace Méthode ajustement Gauss Pesquisa e planejamento estatístico larpcal Regressieanalyse gtt Statistique mathématique - Histoire Statistique mathématique - Histoire ram Tijdreeksen gtt Geschichte Mathematical statistics History Statistik (DE-588)4056995-0 gnd |
| topic_facet | Ajustement relation linéaire Estatística (história) Histoire calcul observation Lineaire analyse Modelos lineares Moindres carrés Méthode Laplace Méthode ajustement Gauss Pesquisa e planejamento estatístico Regressieanalyse Statistique mathématique - Histoire Tijdreeksen Geschichte Mathematical statistics History Statistik |
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