The Sultonov system indicator - page 115

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Dmitry Fedoseev:

5-ю. And why make a smartass out of yourself with all sorts of "open systems", "closed systems", "composite terms", "vectors", "matrices" when everything is explained in 5th grade concepts? In the 5th grade they study systems of linear equations.

Right, right... ;)))))))))))) bragging about your illiteracy -- what else can you do...

 
Олег avtomat:

Yeah, yeah, yeah... ;)))))))))))) you're bragging about your illiteracy -- what else can you do...

Well, there's always an option - you can get your hands on calculus and pretend to be smart by showing graphs and formulas from it.

 
Dmitry Fedoseev:

Well, there is always an option - you can get hold of calculus and pretend to be smart, demonstrating graphs and formulas from it.

Get a mathcaddy - how much cleverness can you show?

 
Alexander Ivanov:
Hi Yusuf and the sittings! 😊
Yusuf, please freeze your robot's signal.
he already said above - the system does not chop and further arguments are irrelevant...
 
Nikolai Semko:

Here's your infamous a0 (aka C0)

White noise is white noise in Africa


I have a feeling that you gave birth to SLAU of 5 equations for years. And you've been dubbing it with a halo of mega-scientific sensation and delusions of grandeur. And that's 7th grade high school maths.

But my tiny SLAU() function easily solves SLAU of 50 equations and I made it and debugged it in less than 1 day. I don't know which way I solved SLAU, because I'm always too lazy to study existing methods, it's easier to invent my own. Most likely my way is not optimal and of course I haven't invented anything new, I'm not strong in theory. But it's the most compact method I've ever seen.

Bravo, you have surpassed Gauss and Kramer:

Consider the linear dependence of the exponent Y on a set of variables x:


To estimate the coefficients of the equation we apply Gauss's method of least squares and obtain the following system of k linear equations with at least n ≥ k+1 groups of actual data Y depending on the values of the variables x:


In general, this system of equations is solved by Gauss (1777- 1855) method of successive elimination of variables or by using the properties of matrices, known as Cramer's method (1704-1752).

Computational complexity

The method of Gauss is a classical method for solvingsystems of linear algebraic equations(SLAE). This is a method of sequential elimination ofvariables, when using the elementary transformation of a system of equations is reduced to an equivalent system of a stepped (or triangular) form, from which consistently, starting with the last (by number) of variables, are all the remaining variables.

The algorithm of solution ofSLAE by Gauss method is divided into two stages.

  • At the first stage the so-called direct course is carried out when byelementary transformations over strings the system is reduced to the stepped ortriangular form, or it is established that the system is incompatible. Namely, among the elements of the first column of the matrix one chooses a non-zero one, moves it to the extreme upper position by permutation of rows and subtracts the first row obtained after permutation from other rows, having multiplied it by the value equal to the ratio of the first element of each of these rows to the first element of the first row, thus zeroing out the column under it. After the above transformations have been made, the first row and the first column are mentally crossed out and continued until a matrix of zero size remains. If at any iteration no nonzero element is found among the elements of the first column, one proceeds to the next column and performs the same operation.
  • At the second stage the so called backward procedure is carried out the essence of which consists in expressing all obtained basic variables through non-basic ones and construct a fundamentalsystem of solutions or, if all variables are basic, express numerically a single solution of the system of linear equations. This procedure starts with the last equation, from which the corresponding basis variable is expressed (and there is only one) and substituted into the previous equations, and so on, going up in "steps". Each line corresponds to exactly one basis variable, so at each step except the last (topmost) one, the situation exactly repeats the case of the last line.

Cramer's methodrequires computation ofdeterminants of appropriate dimension. When usingthe Gaussian methodto compute the determinants, the method has a time complexity of order4, which is worse than ifthe Gaussian methodwere directly used to solve a system of equations.

 
Renat Akhtyamov:
he already said above - the system doesn't chop and further arguments are irrelevant...
Too bad...
So it's not profitable?
 
Renat Akhtyamov:
he already said above - the system doesn't chop and further arguments are irrelevant...

Renat, I never said that. I said that I wouldn't judge until I'd tested everything on a real account. I'm waiting for the advisor to be transferred from MKL5 code to 4.

 
Alexander Ivanov:
Too bad...
So you're not making a profit?

It's too early to tell.

 
Yousufkhodja Sultonov:

It's too early to tell.

It's not too early, it's definitively clear after N. Semko's work. You haven't even done a tenth of it. He formulated it, made an indicator, and published it. And you're still adding X's and Y's.
 
Don't jump to conclusions, brothers. It's all about the wrong platform. They'll move it to 4 and then that's it, then that's it... :D
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