# Estimate vectors from their imprecise sums

I am attempting to approximate specific values of 3 2 - D vectors, $x_1$, $x_2$, and also $x_3$. I have actually made numerous, inaccurate dimensions of their amounts. As an example:

$2x_3 \approx [ 1.157, -73.111]$

$x_2 + x_3 \approx [ 25.184, -55.829]$

$x_2 + 2x_3 \approx [ 26.407, -86.504]$

$2x_1 + x_2 + 3x_3 \approx [ 76.085, -96.201]$

(several, several comparable formulas)

Each dimension has some level of arbitrary mistake. I do not recognize the circulation of these mistakes, so think whatever mistake circulation you such as.

What is an excellent way to approximate the values of these 3 vectors?

Presently I'm approximating my vectors by picking 3 of these dimensions which separate $x_1$, $x_2$, or $x_3$. This overlooks a great deal of details, and also usually leaves me with significant mistake in my price quotes. I'm wishing there is a far better manner in which makes use of even more details from the added dimensions.

Various other details:

I have the specific restraint that the 3 vectors create a triangular:

$x_1 + x_2 + x_3 = 0$ (I could need to turn the indicator of among the vectors to make this real)

Generally, this triangular is close to equilateral, yet not specifically equilateral.

(This inquiry emerged throughout a photo handling trouble in speculative physics. Apologies if this is off - subject, yet it appears extra mathematics than physics to me.)

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2022-06-07 14:35:25
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