[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 536

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You've got to be kidding me. Then at least for the distance, not for the difference in functions.
 
yosuf:

Here is another problem that I managed to solve and if anyone has a ready solution, let's compare:

We need to find formulas for uniquely determining the coefficients a,b and c of an equation with two unknowns by the MNC Gaussian method, if the necessary and unconstrained array of raw data on the values of Y is known with corresponding values of X and Z :

Y = a + bX + cZ


Yusuf, it seems to me that you should already take up the "tasks of the century" for which you get a thousand quid.
 
911:

Yusuf, it seems to me that you should already take up the "tasks of the century" for which you get a thousand quid.
This problem, although not "age-old", is applied and can be found in a number of places. So far the solution is known in the form of a system of normal equations, which is extremely inconvenient.
 
Neutron:

Makes sense.

You can write an identity: N^6=7*10^9 where N is the average number of people you know from a large sample. Therefore N=exp{10/6*ln(10)}=46 people.


Uh... I got even less:

N^6=7*10^9

N = root(7*10^9, 6) = 43.7370687 people.

I checked, 43.7370687^6 really equals 7,000,000,000 :)

 
yosuf: So far, the solution is known in the form of a system of normal equations, which is exceptionally inconvenient.
Yusuf, what is exceptionally inconvenient about this system? Is it because you have forgotten how to solve it?
 
Neutron:


Can I explain the decision in more detail?

 
Mathemat:
Yusuf, what is the exceptional inconvenience of this system? Is it that you have forgotten how to solve it?
Of course it is convenient to come from St. Petersburg to Moscow via Vladivostok every time.
 

You have not answered the question.

The solution to this problem is on the internet, look it up (i.e. the system is solved). The usual ISC.

 
yosuf:

Here is another problem that I managed to solve and if anyone has a ready solution, let's compare:

We need to find formulas for uniquely determining the coefficients a,b and c of an equation with two unknowns by the MNC Gaussian method, if the necessary and unbounded array of raw data on the values of Y is known with corresponding values of X and Z :

Y = a + bX + cZ

The problem in this formulation is standard for a neural network - the MNC error on the sample is minimized. In this case, there is a three-input linear perseptron with a bias on the third input. This is essentially a numerical iterative solution method. How to tie Gaussian here (or not)?

You can not bother in this case with NS and solve the problem by a simple enumeration of coefficients a,b,c minimizing sampling error.

Integer:

I'm ashamed, I don't understand the logic behind your decision... Where does the number 6 come from? Because there are six neighbours?
 
Mathemat:

You have not answered the question.

The solution to this problem is on the internet, look it up (i.e. the system is solved). The usual ISC.

I searched for a long time on the web, all ends up with a system of normal equations, then it is referred to Gauss or Cramer matrix methods. And the solution is very simple and elegant, as in the case of one-factor regression, but apparently, mathematicians were too lazy to reach this simple solution. However, it is true that it is hard to get to the simple stuff.
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