Symbolic-Numeric Integration

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Peter Luschny

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Feb 7, 2022, 7:04:28 AMFeb 7
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That might interest some here:

Symbolic-Numeric Integration of Univariate Expressions based on Sparse Regression https://arxiv.org/abs/2201.12468

nob...@nowhere.invalid

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Feb 11, 2022, 5:30:24 AMFeb 11
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Peter Luschny schrieb:
>
> That might interest some here:
>
> Symbolic-Numeric Integration of Univariate Expressions based on
> Sparse Regression https://arxiv.org/abs/2201.12468
>

The total numbers of indefinite integrals in Table 1 on page 7 do not
agree with the sources; in my files, Hearn's suite comprises 285
integration problems and Timofeev's suite 705 problems. From these
numbers, one computes a modest success rate of 67% for Hearn, and a
disappointingly low 19% for Timofeev. The principle used in selecting
the integration problems must be clearly documented in the paper -
readers will suspect Texas sharpshooting otherwise.

Also, two instances of "Apostle" on page 7 should be corrected to
"Apostol".

Martin.

PS: Are the authors reinventing ancient technology? Their integrator
should perhaps be run against Moses' SIN program.

anti...@math.uni.wroc.pl

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Feb 21, 2022, 4:50:49 PMFeb 21
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Their results are clearly unimpressive. Concerning "ancient",
their idea is closest to parallel integration, also called
Risch-Norman method. There are two main differences:
- they use floating point linear solver instead of rational one
- they use only heuristics instead of structure theorem (+ heuristic)
to build space of candidate integrals.

IIUC correctly they use floating point because they do not have
rational solver. So maybe their method should be called "very
poor man integrator".

--
Waldek Hebisch
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