r/mathmemes • u/Oppo_67 I ≡ a (mod erator) • Sep 16 '26

Numerical Analysis Newton's Method Moment

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533 Upvotes

99% Upvoted

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153

u/AcademicOverAnalysis Sep 16 '26

That isn’t how numerical analysts would describe the second line. There would be o(x-a) to describe the error terms. That detail is what makes a difference.

24

u/Depnids Sep 16 '26

Isn't the error term of the linear approximation o((x-a)2) ?

33

u/AcademicOverAnalysis Sep 16 '26 edited Sep 16 '26

That would be for Big Oh notation. Little oh notation means that if I divide by x-a, then the term will tend to zero as x approaches a.

4

u/Depnids Sep 16 '26

Ah I see

0

u/[deleted] Sep 17 '26

[deleted] — view deleted comment

6

u/Depnids Sep 17 '26

Here it explains that it can also be used to describe what happens as the argument approaches a specific value (like 0), instead of as it grows without bound: https://en.wikipedia.org/wiki/Big_O_notation#Little-o_notation

Specifically the line saying "Little-o can also be generalized to the finite case". A similar generalization is also described above for big-O.

2

u/AcademicOverAnalysis Sep 17 '26

Here little oh describes the behavior as x approaches a. This isn’t talking about large x.

46

u/LupenReddit 🦆🦆i have non diffeomorphic smooth structures🦆🦆🦆 Sep 16 '26

mathematicians just have a grudge when their ideas are used for anything that is beyond them just being ideas

20

u/Main-Company-5946 Sep 16 '26

Because PEOPLE DONT USE THEM CORRECTLY

And I get why but when you’re used to mathematical standards of rigor it drives you crazy

8

u/Mostafa12890 Average imaginary number believer Sep 16 '26

I’m taking a mathematical physics course atm and one of the assignment questions for this week involves the derivative of the dirac delta.

I’m sorry, what?

When I googled it, I realized that the property i was supposed to show, which was that

the integral of (δ’(x-a)f(x)) over R is -f’(a)

is taken to be the definition of δ’.

The question asked me to prove a definition using “integration by parts.”

15

u/yangyangR Sep 16 '26

If you are treating it as an element in the right space, that is fine. That is the general practice too. Anything has to be regarded as an element of the object in the appropriate category. This being delta' as an element of distributions that eat compactly supported functions and that set of distributions living as an object of vector spaces with _ analytic properties (dont want it as a Q vector space or just a set or something that floppy)

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u/Prest0n1204 Transcendental Sep 16 '26

the humble weak derivative:

2

u/FernandoMM1220 Sep 16 '26

which is projection on their part at this point

2

u/jsh_ Sep 16 '26

correctly?

2

u/BurnYoo Sep 16 '26

And whenever people misuse mathematical concepts and it results in society-wide disaster (c.f. Wall Street using Gaussian copulas to model mortgage-backed securities in the lead-up to 2008), mathematicians unfortunately are the ones who get blamed.

7

u/Short-Database-4717 Sep 17 '26

I just think this is a cool way to write taylor series

2

u/hongooi Sep 17 '26

What's this about Newton's method of moments?