Theoria combinationis observationum erroribus minimis obnoxiae: pars prior, pars posterior, supplementum = Theory of the combination of observations least subject to errors
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | Latin English |
| Veröffentlicht: |
Philadelphia
Siam
1995
|
| Schriftenreihe: | Classics in applied mathematics
11 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 241 S. |
| ISBN: | 0898713471 |
Internformat
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| 245 | 1 | 0 | |a Theoria combinationis observationum erroribus minimis obnoxiae |b pars prior, pars posterior, supplementum = Theory of the combination of observations least subject to errors |c by Carl Friedrich Gauss |
| 246 | 1 | 1 | |a Theory of the combination of observations least subject to errors |
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| 490 | 1 | |a Classics in applied mathematics |v 11 | |
| 546 | |a Text teilw. lat., teilw. engl., teilw. dt. | ||
| 650 | 4 | |a Error analysis (Mathematics) | |
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Datensatz im Suchindex
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| adam_text | THEORIA COMBINATIONIS OBSERVATIONUM ERRORIBUS MINIMIS OBNOXIAE PARS
PRIOR * PARS POSTERIOR * SUPPLEMENTUM BY CARL FRIEDRICH GAUSS THEORY OF
THE COMBINATION OF OBSERVATIONS LEAST SUBJECT TO ERRORS PART ONE * PART
TWO * SUPPLEMENT TRANSLATED BY G. W. STEWART UNIVERSITY OF MARYLAND
SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS PHILADELPHIA 1995
CONTENTS TRANSLATOR S INTRODUCTION IX PARS PRIOR/PART ONE* 1 1. RANDOM
AND REGULAR ERRORS IN OBSERVATIONS 3 2. REGULAR ERRORS EXCLUDED; THEIR
TREATMENT 5 3. GENERAL PROPERTIES OF RANDOM ERRORS 5 4. THE DISTRIBUTION
OF THE ERROR 7 5. THE CONSTANT PART OR MEAN VALUE OF THE ERROR 7 6. THE
MEAN SQUARE ERROR AS A MEASURE OF UNCERTAINTY 9 7. MEAN ERROR, WEIGHT,
AND PRECISION 11 8. EFFECT OF REMOVING THE CONSTANT PART 11 9.
INTERPERCENTILE RANGES AND PROBABLE ERROR; PROPERTIES OF THE UNI- 13
FORM, TRIANGULAR, AND NORMAL DISTRIBUTION 10. INEQUALITIES RELATING THE
MEAN ERROR AND INTERPERCENTILE RANGES 15 11. THE FOURTH MOMENTS OF THE
UNIFORM, TRIANGULAR, AND NORMAL 19 DISTRIBUTIONS 12. THE DISTRIBUTION OF
A FUNCTION OF SEVERAL ERRORS 21 13. THE MEAN VALUE OF A FUNCTION OF
SEVERAL ERRORS 21 14. SOME SPECIAL CASES 23 15. CONVERGENCE OF THE
ESTIMATE OF THE MEAN ERROR; THE MEAN ERROR OF 25 THE ESTIMATE ITSELF;
THE MEAN ERROR OF THE ESTIMATE FOR THE MEAN VALUE 16. COMBINING ERRORS
WITH DIFFERENT WEIGHTS 27 17. OVERDETERMINED SYSTEMS OF EQUATIONS; THE
PROBLEM OF OBTAINING 31 THE UNKNOWNS AS COMBINATIONS OF OBSERVATIONS;
THE PRINCIPLE OF LEAST SQUARES 18. THE MEAN ERROR OF A FUNCTION OF
QUANTITIES WITH ERRORS 33 19. THE REGRESSION MODEL 37 20. THE BEST
COMBINATION FOR ESTIMATING THE FIRST UNKNOWN 39 21. THE WEIGHT OF THE
ESTIMATE; ESTIMATES OF THE REMAINING UNKNOWNS 43 AND THEIR WEIGHTS;
JUSTIFICATION OF THE PRINCIPLE OF LEAST SQUARES 22. THE CASE OF A SINGLE
UNKNOWN; THE ARITHMETIC MEAN 45 PARS POSTERIOR/PART TWO 49 23. EXISTENCE
OF THE LEAST SQUARES ESTIMATES 51 24. RELATION BETWEEN COMBINATIONS FOR
DIFFERENT UNKNOWNS 53 THE TITLES OF THE NUMBERED ARTICLES ARE THE
TRANSLATOR S AND ARE INTENDED TO HELP ORIENT THE READER. THEY DO NOT
APPEAR IN THE NUMBERED ARTICLES. VI CONTENTS 25. A FORMULA FOR THE
RESIDUAL SUM OF SQUARES 55 26. ANOTHER FORMULA FOR THE RESIDUAL SUM OF
SQUARES 57 27. FOUR FORMULAS FOR THE RESIDUAL SUM OF SQUARES AS A
FUNCTION OF 57 THE UNKNOWNS 28. ERRORS IN THE LEAST SQUARES ESTIMATES AS
FUNCTIONS OF THE ERRORS 59 IN THE OBSERVATIONS; MEAN ERRORS AND
CORRELATIONS 29. LINEAR FUNCTIONS OF THE UNKNOWNS 61 30. LEAST SQUARES
WITH A LINEAR CONSTRAINT 63 31. REVIEW OF GAUSSIAN ELIMINATION 67 32.
ABBREVIATED COMPUTATION OF THE WEIGHTS OF THE UNKNOWNS 69 33.
COMPUTATIONAL DETAILS 71 34. ABBREVIATED COMPUTATION OF THE WEIGHT OF A
LINEAR FUNCTION OF 75 THE UNKNOWNS 35. UPDATING THE UNKNOWNS AND THEIR
WEIGHTS WHEN A NEW OBSERVA- 77 TION IS ADDED TO THE SYSTEM 36. UPDATING
THE UNKNOWNS AND THEIR WEIGHTS WHEN THE WEIGHT OF 83 AN OBSERVATION
CHANGES 37. A BAD FORMULA FOR ESTIMATING THE ERRORS IN THE OBSERVATIONS
FROM 83 THE RESIDUAL SUM OF SQUARES 38. THE CORRECT FORMULA 87 39. THE
MEAN ERROR OF THE RESIDUAL SUM OF SQUARES 89 40. INEQUALITIES FOR THE
MEAN ERROR OF THE RESIDUAL SUM OF SQUARES; 95 THE CASE OF THE NORMAL
DISTRIBUTION SUPPLEMENTUM/SUPPLEMENT 99 1. PROBLEMS HAVING CONSTRAINTS
ON THE OBSERVATIONS; REDUCTION TO 101 AN ORDINARY LEAST SQUARES PROBLEM
2. FUNCTIONS OF THE OBSERVATIONS; THEIR MEAN ERRORS 103 3. ESTIMATING A
FUNCTION OF OBSERVATIONS THAT ARE SUBJECT TO 105 CONSTRAINTS 4.
CHARACTERIZATION OF PERMISSIBLE ESTIMATES 107 5. THE FUNCTION THAT GIVES
THE MOST RELIABLE ESTIMATE 109 6. THE VALUE OF THE MOST RELIABLE
ESTIMATE 111 7. FOUR FORIHULAS FOR THE WEIGHT OF THE VALUE OF THE
ESTIMATE 113 8. THE CASE OF MORE THAN ONE FUNCTION 115 9. THE MOST
RELIABLE ADJUSTMENTS OF THE OBSERVATIONS AND THEIR USE 119 IN ESTIMATION
10. LEAST SQUARES CHARACTERIZATION OF THE MOST RELIABLE ADJUSTMENT 11.
DIFFICULTIES IN DETERMINING WEIGHTS 12. A BETTER METHOD 13.
COMPUTATIONAL DETAILS CONTENTS VII 14. EXISTENCE OF THE ESTIMATES 127
15. ESTIMATING THE MEAN ERROR IN THE OBSERVATIONS 131 16. ESTIMATING THE
MEAN ERROR IN THE OBSERVATIONS, CONTINUED 135 17. THE MEAN ERROR IN THE
ESTIMATE 137 18. INCOMPLETE ADJUSTMENT OF OBSERVATIONS 137 19. RELATION
BETWEEN COMPLETE AND INCOMPLETE ADJUSTMENTS 139 20. A BLOCK ITERATIVE
METHOD FOR ADJUSTING OBSERVATIONS 141 21. THE INVERSE OF A SYMETRIC
SYSTEM IS SYMMETRIC 143 22. FUNDAMENTALS OF GEODESY 147 23. DE
KRAYENHOF S TRIANGULATION 149 24. A TRIANGULATION FROM HANNOVER 159 25.
DETERMINING WEIGHTS IN THE HANNOVER TRIANGULATION 167 ANZEIGEN/NOTICES
173 PART ONE 175 PART TWO 187 SUPPLEMENT 195 AFTERWORD 205 GAUSS S
SCHOOLDAYS 207 LEGENDRE AND THE PRIORITY CONTROVERSY 210 BEGINNINGS:
MAYER, BOSCOVICH, AND LAPLACE 211 GAUSS AND LAPLACE 214 THE THEORIA
MOTUS 214 LAPLACE AND THE CENTRAL LIMIT THEOREM 217 THE THEORIA
COMBINATIONIS OBSERVATIONUM 220 THE PRECISION OF OBSERVATIONS 220 THE
COMBINATION OF OBSERVATIONS 223 THE INVERSION OF LINEAR SYSTEMS 225
GAUSSIAN ELIMINATION AND NUMERICAL LINEAR ALGEBRA 227 THE GENERALIZED
MINIMUM VARIANCE THEOREM 232 REFERENCES 237
|
| any_adam_object | 1 |
| author | Gauß, Carl Friedrich 1777-1855 |
| author_GND | (DE-588)104234644 |
| author_facet | Gauß, Carl Friedrich 1777-1855 |
| author_role | aut |
| author_sort | Gauß, Carl Friedrich 1777-1855 |
| author_variant | c f g cf cfg |
| building | Verbundindex |
| bvnumber | BV010848424 |
| classification_rvk | SG 600 SK 910 |
| ctrlnum | (OCoLC)473163135 (DE-599)BVBBV010848424 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV010848424 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:59:54Z |
| institution | BVB |
| isbn | 0898713471 |
| language | Latin English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007251024 |
| oclc_num | 473163135 |
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| owner | DE-384 DE-703 DE-83 DE-634 DE-Aug4 |
| owner_facet | DE-384 DE-703 DE-83 DE-634 DE-Aug4 |
| physical | XI, 241 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Siam |
| record_format | marc |
| series | Classics in applied mathematics |
| series2 | Classics in applied mathematics |
| spelling | Gauß, Carl Friedrich 1777-1855 Verfasser (DE-588)104234644 aut Theoria combinationis observationum erroribus minimis obnoxiae pars prior, pars posterior, supplementum = Theory of the combination of observations least subject to errors by Carl Friedrich Gauss Theory of the combination of observations least subject to errors Philadelphia Siam 1995 XI, 241 S. txt rdacontent n rdamedia nc rdacarrier Classics in applied mathematics 11 Text teilw. lat., teilw. engl., teilw. dt. Error analysis (Mathematics) Least squares Methode der kleinsten Quadrate (DE-588)4038974-1 gnd rswk-swf Methode der kleinsten Quadrate (DE-588)4038974-1 s DE-604 Classics in applied mathematics 11 (DE-604)BV008258410 11 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007251024&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gauß, Carl Friedrich 1777-1855 Theoria combinationis observationum erroribus minimis obnoxiae pars prior, pars posterior, supplementum = Theory of the combination of observations least subject to errors Classics in applied mathematics Error analysis (Mathematics) Least squares Methode der kleinsten Quadrate (DE-588)4038974-1 gnd |
| subject_GND | (DE-588)4038974-1 |
| title | Theoria combinationis observationum erroribus minimis obnoxiae pars prior, pars posterior, supplementum = Theory of the combination of observations least subject to errors |
| title_alt | Theory of the combination of observations least subject to errors |
| title_auth | Theoria combinationis observationum erroribus minimis obnoxiae pars prior, pars posterior, supplementum = Theory of the combination of observations least subject to errors |
| title_exact_search | Theoria combinationis observationum erroribus minimis obnoxiae pars prior, pars posterior, supplementum = Theory of the combination of observations least subject to errors |
| title_full | Theoria combinationis observationum erroribus minimis obnoxiae pars prior, pars posterior, supplementum = Theory of the combination of observations least subject to errors by Carl Friedrich Gauss |
| title_fullStr | Theoria combinationis observationum erroribus minimis obnoxiae pars prior, pars posterior, supplementum = Theory of the combination of observations least subject to errors by Carl Friedrich Gauss |
| title_full_unstemmed | Theoria combinationis observationum erroribus minimis obnoxiae pars prior, pars posterior, supplementum = Theory of the combination of observations least subject to errors by Carl Friedrich Gauss |
| title_short | Theoria combinationis observationum erroribus minimis obnoxiae |
| title_sort | theoria combinationis observationum erroribus minimis obnoxiae pars prior pars posterior supplementum theory of the combination of observations least subject to errors |
| title_sub | pars prior, pars posterior, supplementum = Theory of the combination of observations least subject to errors |
| topic | Error analysis (Mathematics) Least squares Methode der kleinsten Quadrate (DE-588)4038974-1 gnd |
| topic_facet | Error analysis (Mathematics) Least squares Methode der kleinsten Quadrate |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007251024&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008258410 |
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