Iterative methods for linear systems of equations: A brief historical journey Article Swipe
This paper presents a brief historical survey of iterative methods for solving linear systems of equations. The journey begins with Gauss who developed the first known method that can be termed iterative. The early 20th century saw good progress of these methods which were initially used to solve least-squares systems, and then linear systems arising from the discretization of partial different equations. Then iterative methods received a big impetus in the 1950s - partly because of the development of computers. The survey does not attempt to be exhaustive. Rather, the aim is to underline the way of thinking at a specific time and to highlight the major ideas that steered the field.
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Metadata
- Type
- preprint
- Language
- en
- Landing Page
- https://doi.org/10.1090/conm/754/15141
- OA Status
- green
- Cited By
- 3
- References
- 38
- Related Works
- 20
- OpenAlex ID
- https://openalex.org/W2965248848
All OpenAlex metadata
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- OpenAlex ID
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https://openalex.org/W2965248848Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.1090/conm/754/15141Digital Object Identifier
- Title
-
Iterative methods for linear systems of equations: A brief historical journeyWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2020Year of publication
- Publication date
-
2020-01-01Full publication date if available
- Authors
-
Yousef SaadList of authors in order
- Landing page
-
https://doi.org/10.1090/conm/754/15141Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/1908.01083Direct OA link when available
- Concepts
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Iterative method, Linear system, Gauss, Discretization, Field (mathematics), Applied mathematics, Computer science, System of linear equations, Linear equation, Mathematics, Calculus (dental), Mathematical optimization, Mathematical analysis, Physics, Medicine, Quantum mechanics, Dentistry, Pure mathematicsTop concepts (fields/topics) attached by OpenAlex
- Cited by
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3Total citation count in OpenAlex
- Citations by year (recent)
-
2023: 2, 2022: 1Per-year citation counts (last 5 years)
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38Number of works referenced by this work
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20Other works algorithmically related by OpenAlex
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| abstract_inverted_index.partial | 59 |
| abstract_inverted_index.solving | 11 |
| abstract_inverted_index.steered | 109 |
| abstract_inverted_index.systems | 13, 53 |
| abstract_inverted_index.presents | 2 |
| abstract_inverted_index.progress | 38 |
| abstract_inverted_index.received | 65 |
| abstract_inverted_index.specific | 100 |
| abstract_inverted_index.systems, | 49 |
| abstract_inverted_index.thinking | 97 |
| abstract_inverted_index.developed | 22 |
| abstract_inverted_index.different | 60 |
| abstract_inverted_index.highlight | 104 |
| abstract_inverted_index.initially | 44 |
| abstract_inverted_index.iterative | 8, 63 |
| abstract_inverted_index.underline | 93 |
| abstract_inverted_index.computers. | 79 |
| abstract_inverted_index.equations. | 15, 61 |
| abstract_inverted_index.historical | 5 |
| abstract_inverted_index.iterative. | 31 |
| abstract_inverted_index.development | 77 |
| abstract_inverted_index.exhaustive. | 87 |
| abstract_inverted_index.least-squares | 48 |
| abstract_inverted_index.discretization | 57 |
| cited_by_percentile_year | |
| corresponding_author_ids | https://openalex.org/A5016419713 |
| countries_distinct_count | 0 |
| institutions_distinct_count | 1 |
| citation_normalized_percentile |