Corecursive Coding of High Computational Derivatives and Power Series
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916579198894080 |
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| author | Karczmarczuk, Jerzy |
| author_facet | Karczmarczuk, Jerzy |
| contents | We discuss the functional lazy techniques in generation and handling of arbitrarily long sequences of derivatives of numerical expressions in one ``variable''; the domain to which the paper belongs is usually nicknamed ``Automatic differentiation''. Two models thereof are considered, the chains of ``pure'' derivatives, and the infinite power series, similar, but algorithmically a bit different. We deal with their arithmetic/algebra, and with more convoluted procedures, such as composition and reversion. Some more specific applications of these structures are also presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_13194 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Corecursive Coding of High Computational Derivatives and Power Series Karczmarczuk, Jerzy Programming Languages Data Structures and Algorithms D.3.3 We discuss the functional lazy techniques in generation and handling of arbitrarily long sequences of derivatives of numerical expressions in one ``variable''; the domain to which the paper belongs is usually nicknamed ``Automatic differentiation''. Two models thereof are considered, the chains of ``pure'' derivatives, and the infinite power series, similar, but algorithmically a bit different. We deal with their arithmetic/algebra, and with more convoluted procedures, such as composition and reversion. Some more specific applications of these structures are also presented. |
| title | Corecursive Coding of High Computational Derivatives and Power Series |
| topic | Programming Languages Data Structures and Algorithms D.3.3 |
| url | https://arxiv.org/abs/2501.13194 |