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Theory of the combination of observations least subject to error : part one, part two, supplement = Theoria combinationis observationum erroribus minimus obnoxiae : pars prior, pars posterior, supplementum

Author: Carl Friedrich Gauss; G W Stewart
Publisher: Philadelphia : Society for Industrial and Applied Mathematics, 1995.
Series: Classics in applied mathematics, 11.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:

English translation of Gauss' two memoirs which contain his final, definitive treatment of least squares and wealth of additional material.

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Carl Friedrich Gauss; G W Stewart
ISBN: 0898713471 9780898713473
OCLC Number: 32133323
Description: xi, 241 pages ; 26 cm.
Contents: Part 1: --
1. Random and regular errors in observations --
2. Regular errors excluded; their treatment --
3. General properties of random errors --
4. The distribution of the error --
5. The constant part or mean value of the error --
6. The mean square error as a measure of uncertainty --
7. Mean error, weight, and precision --
8. Effect of removing the constant part --
9. Interpercentile ranges and probable error; properties of the uniform, triangular, and normal distribution --
10. Inequalities relating the mean error and interpercentile ranges --
11. The fourth moments of the uniform, triangular, and normal distributions --
12. The distribution of a function of several errors --
13. The mean value of a function of several errors --
14. Some special cases --
15. Convergence of the estimate of the mean error; the mean error of the estimate itself; the mean error of the estimate for the mean value --
16. Combining errors with different weights --
17. Overdetermined systems of equations; the problem of obtaining the unknowns as combinations of observations; the principle of least squares --
18. The mean error of a function of quantities with errors --
19. The regression model --
20. The best combination for estimating the first unknown --
21. The weight of the estimate; estimates of the remaining unknowns and their weights; justification of the principle of least squares --
22. The case of a single unknown; the arithmetic mean --
Part 2: --
23. Existence of the least squares estimates --
24. Relation between combinations for different unknowns --
25. A formula for the residual sum of squares --
26. Another formula for the residual sum of squares --
27. Four formulas for the residual sum of squares as a function of the unknowns --
28. Errors in the least squares estimates as functions of the errors in the observations; mean errors and correlations --
29. Linear functions of the unknowns --
30. Least squares with a linear constraint --
31. Review of Gaussian elimination --
32. Abbreviated computation of the weights of the unknowns --
33. Computational details --
34. Abbreviated computation of the weight of a linear function of the unknowns --
35. Updating the unknowns and their weights when a new observation is added to the system --
36. Updating the unknowns and their weights when the weight of an observation changes --
37. A bad formula for estimating the errors in the observations from the residual sum of squares --
38. The correct formula --
39. The mean error of the residual sum of squares --
40. Inequalities for the mean error of the residual sum of squares; the case of the normal distribution --
Supplement: --
1. Problems having constraints on the observations; reduction to an ordinary least squares problem --
2. Functions of the observations; their mean errors --
3. Estimating a function of observations that are subject to constraints --
4. Characterization of permissible estimates --
5. The function that gives the most reliable estimate --
6. The value of the most reliable estimate --
7. Four formulas for the weight of the value of the estimate --
8. The case of more than one function --
9. The most reliable adjustments of the observations and their use in estimation --
10. Least squares characterizaton of the most reliable adjustment --
11. Difficulties in determining weights --
12. A better method --
13. Computational details --
14. Existence of the estimates --
15. Estimating the mean error in the observations --
16. Estimating the mean error in the observations, continued --
17. The mean error in the estimate --
18. Incomplete adjustment of observations --
19. Relation between complete and incomplete adjustments --
20. A block iterative method for adjusting observations --
21. The inverse of a symetric system is symmetric --
22. Fundamentals of geodesy --
23. De Krayenhof's triangulation --
24. A triangulation from Hannover --
25. Determining weights in the Hannover triangulation.
Series Title: Classics in applied mathematics, 11.
Other Titles: Theoria combinationis observationum erroribus minimis obnoxiae.
Theoria combinationis observationum erroribus minimus obnoxiae
Responsibility: by Carl Friedrich Gauss ; translated by G.W. Stewart.
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