Wikidata:Property proposal/iterative approximation

iterative approximation

Originally proposed at Wikidata:Property proposal/Natural science

   Withdrawn

Description	An expression that can be used to generate a sequence of improving approximate solutions from initial values.
Represents	iterative numerical method (Q2321565)
Data type	Mathematical expression
Example 1	Lambert W function (Q429331) → $w_{j+1}=w_{j}-{\frac {w_{j}e^{w_{j}}-z}{e^{w_{j}}+w_{j}e^{w_{j}}}}$
Example 2	square root of 2 (Q389813) → $a_{n+1}={\frac {a_{n}+{\frac {2}{a_{n}}}}{2}}={\frac {a_{n}}{2}}+{\frac {1}{a_{n}}}$
Example 3	Gauss–Newton algorithm (Q1496373) → ${\boldsymbol {\beta }}^{(s+1)}={\boldsymbol {\beta }}^{(s)}-\left(\mathbf {J_{r}} ^{\mathsf {T}}\mathbf {J_{r}} \right)^{-1}\mathbf {J_{r}} ^{\mathsf {T}}\mathbf {r} \left({\boldsymbol {\beta }}^{(s)}\right)$
Expected completeness	always incomplete (Q21873886)
See also	defining formula (P2534) approximation algorithm (P1171)
Wikidata project	WikiProject Mathematics (Q8487137)

Motivation

Iterative approximation is an important property of mathematics. Midleading (talk) 08:15, 10 August 2022 (UTC)

Discussion

•  Support Sure. ArthurPSmith (talk) 18:34, 11 August 2022 (UTC)
•  Support --Tinker Bell ★ ♥ 04:46, 16 August 2022 (UTC)
•  Comment Can we see examples besides the Lambert W function? What classes of items does this property apply to? The obvious ones would be functions and numeric values, but there are probably others. Also, it seems like the expected completeness would be always incomplete (Q21873886) since there can be multiple (infinite?) iterative approximations for infinitely many different values. — The Erinaceous One 🦔 04:03, 6 September 2022 (UTC)

I have updated the examples and expected completeness, thank you! --Midleading (talk) 08:36, 9 September 2022 (UTC)

•  Oppose I am not convinced the proposed property serves a purpose not already fulfilled by defining formula (P2534). In the case of Gauss–Newton algorithm (Q1496373) and other algorithms, the proposed property would be incorrect since the algorithm is not being approximated—it should instead be

Gauss–Newton algorithm (Q1496373)defining formula (P2534)'${\boldsymbol {\beta }}^{(s+1)}={\boldsymbol {\beta }}^{(s)}-\left(\mathbf {J_{r}} ^{\mathsf {T}}\mathbf {J_{r}} \right)^{-1}\mathbf {J_{r}} ^{\mathsf {T}}\mathbf {r} \left({\boldsymbol {\beta }}^{(s)}\right)$'.

For the examples of the proposed property for functions and numbers, I have concerns about the notability of the formulas. Would any correct statement be acceptable? If there is iterative approximation algorithm for computing a value that is notworthy than shouldn't that algorithm have its own item? Creating links using approximation algorithm (P1171) creates richer structured data about the approximation algorithm (side note: it looks like P1171 could use some love---it only has 9 uses and they are all for pi (Q167)!). Then we should just use defining formula (P2534) as in the case of Gauss–Newton algorithm (Q1496373). — The Erinaceous One 🦔 08:56, 10 September 2022 (UTC) (P.S., I removed the "ready" status while we are still discussing.)

The example for Lambert W function (Q429331) is derived from Newton's method (Q374195) which can also be applied to many other problems. The specific formula used is likely more relevant than a generic information about Newton's method (Q374195) can approximate Lambert W function (Q429331). One of Newton's method (Q374195) and the formula $w_{j+1}=w_{j}-{\frac {w_{j}e^{w_{j}}-z}{e^{w_{j}}+w_{j}e^{w_{j}}}}$ can be added as a qualifier of another one. But there is always a possibility that there is no Wikidata item for an algorithm used (such as the more efficient approximations published on a journal article). Only noteworthy formulas (relatively simple, efficient, well-known or having a reference) should be added. I agree Gauss–Newton algorithm (Q1496373) can use defining formula (P2534). --Midleading (talk) 09:53, 10 September 2022 (UTC)

Maybe it would be better to provide the approximation formula as a qualifier on a approximation algorithm (P1171) statement: Lambert W function (Q429331)approximation algorithm (P1171)Newton's method (Q374195)defining formula (P2534)$w_{j+1}=w_{j}-{\frac {w_{j}e^{w_{j}}-z}{e^{w_{j}}+w_{j}e^{w_{j}}}}$. If there is no Wikidata item for the P1171 statement to point to, then a new item can easily be created. — The Erinaceous One 🦔 06:57, 12 September 2022 (UTC)

I added Lambert W function (Q429331)approximation algorithm (P1171)Newton's method (Q374195). It looks like this is not the correct property usage. Midleading (talk) 09:30, 14 September 2022 (UTC)

I added a comment on the talk page for P1171 to expand the type constraints. — The Erinaceous One 🦔 18:45, 14 September 2022 (UTC)

I've decided that approximation algorithm (P1171) is better. Midleading (talk) 02:52, 19 November 2022 (UTC)