Digital Library of Zielona Góra contains 63 052 digital objects
Object
Title: Non-standard analysis revisited: An easy axiomatic presentation oriented towards numerical applications
Contributor:
Korbicz, Józef (1951- ) - red. ; Uciński, Dariusz - red.
Group publication title:
Abstract:
Alpha-Theory was introduced in 1995 to provide a simplified version of Robinson`s non-standard analysis which overcomes the technicalities of symbolic logic. The theory has been improved over the years, and recently it has been used also to solve practical problems in a pure numerical way, thanks to the introduction of algorithmic numbers. In this paper, we introduce Alpha-Theory using a novel axiomatic approach oriented towards real-world applications, to avoid the need to master mathematical logic and model theory. ; To corroborate the strong link of this Alpha-Theory axiomatization and scientific computations, we report numerical illustrative applications never carried out by means of non-standard numbers within a computer, i.e., the computation of the eigenvalues of a non-Archimedean matrix, some computations related to non-Archimedean Markov chains, and the Cholesky factorization of a non-Archimedean matrix. We also highlight the differences between our numerical routines and pure symbolic approaches: as expected, the former scales better when the dimension of the problem increases.
Publisher:
Zielona Góra: Uniwersytet Zielonogórski
Resource Identifier:
DOI:
Pages:
Source:
AMCS, volume 32, number 1 (2022) ; click here to follow the link
Language:
License CC BY 4.0:
Rights:
Biblioteka Uniwersytetu Zielonogórskiego
Object collections:
- Digital Library of Zielona Góra > Repository > Faculties > Faculty of Computer, Electrical and Control Engineering
- Digital Library of Zielona Góra > Repository > Types of work > Articles
- Digital Library of Zielona Góra > Repository > Scientific journals and UZ publishing series > International Journal of Applied Mathematics and Computer Science (AMCS) > International Journal of Applied Mathematics and Computer Science (AMCS) (2022)
Last modified:
Jul 22, 2025
In our library since:
Jul 22, 2025
Number of object content hits:
19
All available object's versions:
https://zbc.uz.zgora.pl/publication/101430
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 32, number 1 (2022)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 32, number 2 (2022)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 32, number 3 (2022)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 32, number 4 (2022)
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| Edition name | Date |
|---|---|
| Non-standard analysis revisited: An easy axiomatic presentation oriented towards numerical applications | Jul 22, 2025 |
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