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The discussion centers on understanding specific equations from two attached files related to linear stochastic inverse problem theory. The user seeks clarification on the method of least squares in equation 47 from "image 1" and the derivation of equation 52 and its subsequent equation 53 from "image 2." Recommendations for resources include a helpful MIT lecture that enhances understanding of the concepts and Tarantola's book for a deeper dive into inverse problem theory. Additionally, "An Introduction to Optimal Estimation" by Liebelt is suggested for those interested in an engineering perspective. Engaging with these resources may provide the clarity needed on the discussed equations.
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Hello. I can't understand some things in these two files attached with this thread.
Firstly,in file "image 1",i don't know about the method of least sequares mentioned in equation 47.

Secondly, in file "image 2",from where the equation 52 comes and how do we get the next equation 53.

I want to discuss about these two pages if there's anyone already knows about this field or has special experience with it.

thanks.
 

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This is linear stochastic inverse problem theory. Here is a great MIT graduate video lecture that explains it pretty well (lecture 4). The geometric perspective he explains at around 17 mins in really helped my intuition about it.
http://ocw.mit.edu/OcwWeb/Mathematics/18-085Fall-2007/VideoLectures/index.htm

If you want to really understand inverse problem theory, I recommend you Tarantola's book (you can download the pdf from the authors site):
http://www.ipgp.jussieu.fr/~tarantola/Files/Professional/Books/index.html

"Liebelt, P. B., 1967, An introduction to optimal estimation" is also alright (this one is much more of an engineering perspective)
 
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This is really amazing. Thanks.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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