/sci/ - Science & Math » Thread #11242123

23KiB, 836x218, Capture+_2019-12-21-09-24-05-1.png

View Same Google iqdb SauceNAO

Anonymous Sat 21 Dec 01:30:36 2019 No.11242123 View Reply Original Report

Quoted By: >>11243345 >>11245115 >>11245410 >>11245471

I try to apply the best approximation theorem with this proble but I am still not sure if I am correct. In addition, the constant (c) bothers.

Anonymous

Anonymous Sat 21 Dec 2019 01:56:01 No.11242181 Report

Quoted By: >>11242184

Helllllllp. I need someone who I can brainstorm with.

Anonymous

Anonymous Sat 21 Dec 2019 01:57:26 No.11242184 Report

Quoted By:

>>11242181
>brainstorm
>babby convex optimization
Did you try just expanding the inner product?

Anonymous

Anonymous Sat 21 Dec 2019 16:39:00 No.11243339 Report

Quoted By:

that's just how you define the distance of u to the span of v, it's trivial

Anonymous

Anonymous Sat 21 Dec 2019 16:41:05 No.11243340 Report

Quoted By:

>>>/sci/sqt/

Anonymous

Anonymous Sat 21 Dec 2019 16:45:06 No.11243345 Report

Quoted By:

>>11242123
remind yourself what the component of u along v is

Anonymous

Anonymous Sun 22 Dec 2019 07:38:41 No.11245115 Report

Quoted By: >>11245320

>>11242123
first understand what the mathematical expression is saying and go from there. Its intuitively obvious the statement it true; it says the length of some vector u minus the projection of another vector v onto u is always less than or equal to the length of the vector u minus the vector c*v where c is a constant. this makes sense for a small c so I would try a few rough sketches to see if you can find an equation relating the length of c,u, and v so you can write down the constraint on c for the equality to be true.

Anonymous

Anonymous Sun 22 Dec 2019 10:33:17 No.11245320 Report

Quoted By: >>11246371

>>11245115
It's the projection of u onto v, isn't it?

Anonymous

Anonymous Sun 22 Dec 2019 11:41:17 No.11245410 Report

Quoted By:

>>11242123
do you understand what does the theorem actually say ? have you tried drawing a picture ?

Anonymous

Anonymous Sun 22 Dec 2019 12:35:34 No.11245471 Report

Quoted By: >>11246400 >>11246662 >>11246819

>>11242123
1. minimalize $|u-cv|^2 = \langle u-cv,u-cv \rangle$ by baby calculus (take derivative with respect to $c$ , obtain condition for $c$ )
2. any projection of $u$ onto $v$ has the form $\text{proj}_v u = cv$ . derive a condition for $c$ so that this projection is orthogonal.
3. compare those two conditions.

Anonymous

Anonymous Sun 22 Dec 2019 21:53:47 No.11246371 Report

Quoted By:

>>11245320
sry yes

Anonymous

Anonymous Sun 22 Dec 2019 22:17:11 No.11246400 Report

Quoted By:

>>11245471
>derivative w/ respect to c
illegal.

Anonymous

Anonymous Mon 23 Dec 2019 00:06:25 No.11246589 Report

Quoted By:

I don't quite understand this from an intuition standpoint. The projecting yields something proportional to v, say kv. Why should the righthand side be larger than that for every c?

Anonymous

Anonymous Mon 23 Dec 2019 00:42:49 No.11246662 Report

Quoted By:

>>11245471
Beat me to it!.

Anonymous

View Same Google iqdb SauceNAO 79578280_466452614268796_8306752 (...).jpg, 17KiB, 480x640

Anonymous Mon 23 Dec 2019 01:57:01 No.11246819 Report

Quoted By:

>>11245471

Capcode	All Only User Posts Only Moderator Posts Only Admin Posts Only Developer Posts
Show Posts	All Only With Images Only Without Images
Deleted Posts	All Only Deleted Posts Only Non-Deleted Posts
Ghost Posts	All Only Ghost Posts Only Non-Ghost Posts
Post Type	All Only Sticky Threads Only Opening Posts Only Reply Posts
Results	All Grouped By Threads
Order	Latest Posts First Oldest Posts First

Your latest searches