A note on the use of Gauss' formulas in non-linear goedetic adjustment.
The theory of adjustment is usually expounded by algebraic and analytical methods. It is well known, however, that the theory of linear adjustment can be represented simply and directly, using geometric reasoning, as properties of linear spaces. In Geodesy, geometric reasoning was already advocated...
| Main Author: | |
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| Format: | Journal Article |
| Language: | English |
| Published: |
1985
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| Online Access: | http://hdl.handle.net/20.500.11937/5432 |
| _version_ | 1848744795207368704 |
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| author | Teunissen, Peter |
| author_facet | Teunissen, Peter |
| author_sort | Teunissen, Peter |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | The theory of adjustment is usually expounded by algebraic and analytical methods. It is well known, however, that the theory of linear adjustment can be represented simply and directly, using geometric reasoning, as properties of linear spaces. In Geodesy, geometric reasoning was already advocated by Tienstrat (1948), who used the Ricci calculus. Generalizing, the theory of non-linear adjustment can then be represented as properties of curved manifolds. In this note we show the principal role played by Gauss' formulas, known from differential geometry, in Gauss' method of least-squares. In particular we show the significance of AMS 1980 subject classification: 62P99, 62F10, 86A30. |
| first_indexed | 2025-11-14T06:07:08Z |
| format | Journal Article |
| id | curtin-20.500.11937-5432 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T06:07:08Z |
| publishDate | 1985 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-54322017-10-02T02:27:19Z A note on the use of Gauss' formulas in non-linear goedetic adjustment. Teunissen, Peter The theory of adjustment is usually expounded by algebraic and analytical methods. It is well known, however, that the theory of linear adjustment can be represented simply and directly, using geometric reasoning, as properties of linear spaces. In Geodesy, geometric reasoning was already advocated by Tienstrat (1948), who used the Ricci calculus. Generalizing, the theory of non-linear adjustment can then be represented as properties of curved manifolds. In this note we show the principal role played by Gauss' formulas, known from differential geometry, in Gauss' method of least-squares. In particular we show the significance of AMS 1980 subject classification: 62P99, 62F10, 86A30. 1985 Journal Article http://hdl.handle.net/20.500.11937/5432 en restricted |
| spellingShingle | Teunissen, Peter A note on the use of Gauss' formulas in non-linear goedetic adjustment. |
| title | A note on the use of Gauss' formulas in non-linear goedetic adjustment. |
| title_full | A note on the use of Gauss' formulas in non-linear goedetic adjustment. |
| title_fullStr | A note on the use of Gauss' formulas in non-linear goedetic adjustment. |
| title_full_unstemmed | A note on the use of Gauss' formulas in non-linear goedetic adjustment. |
| title_short | A note on the use of Gauss' formulas in non-linear goedetic adjustment. |
| title_sort | note on the use of gauss' formulas in non-linear goedetic adjustment. |
| url | http://hdl.handle.net/20.500.11937/5432 |