An elementary approach to splittings of unbounded operators
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916089230786560 |
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| author | Iserles, Arieh Kropielnicka, Karolina |
| author_facet | Iserles, Arieh Kropielnicka, Karolina |
| contents | Using elementary means, we derive the three most popular splittings of $e^{(A+B)}$ and their error bounds in the case when $A$ and $B$ are (possibly unbounded) operators in a Hilbert space, generating strongly continuous semigroups, $e^{tA}$, $e^{tB}$ and $e^{t(A+B)}$. The error of these splittings is bounded in terms of the norm of the commutators $[A, B]$, $[A, [A, B]]$ and $[B, [A, B]]$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06635 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An elementary approach to splittings of unbounded operators Iserles, Arieh Kropielnicka, Karolina Functional Analysis Numerical Analysis Primary 65J10, Secondary 65M15 Using elementary means, we derive the three most popular splittings of $e^{(A+B)}$ and their error bounds in the case when $A$ and $B$ are (possibly unbounded) operators in a Hilbert space, generating strongly continuous semigroups, $e^{tA}$, $e^{tB}$ and $e^{t(A+B)}$. The error of these splittings is bounded in terms of the norm of the commutators $[A, B]$, $[A, [A, B]]$ and $[B, [A, B]]$. |
| title | An elementary approach to splittings of unbounded operators |
| topic | Functional Analysis Numerical Analysis Primary 65J10, Secondary 65M15 |
| url | https://arxiv.org/abs/2401.06635 |