Interpolation, approximation and the like (alglib package) - page 7
You are missing trading opportunities:
- Free trading apps
- Over 8,000 signals for copying
- Economic news for exploring financial markets
Registration
Log in
You agree to website policy and terms of use
If you do not have an account, please register
This is best served by my URMhttps://www.mql5.com/ru/articles/250
read diagonally, didn't see any similar words. It's more like https://www.mql5.com/ru/articles/412
but I can't make it out.
My URMhttps://www.mql5.com/ru/articles/250 would be best suited for this, although I am not in favour of neural networks.
That's not a fact. No one has figured out what the problem is yet and you already have a solution.
That's not a fact. No one has figured out what the problem is yet, and you already have a solution.
Yes, everyone has figured it out, they just don't know how to do
Random transformation of features for a neural network, as an output function, so that new data can be substituted
Everyone has figured it out, they just don't know how to do
a random transformation of features for the neural network, as an output function, so that new data can be substituted
Mm-hmm. Everyone understands, but can't say.
You don't seem to have practically solved the problem of interpolation, do you? Yes? In interpolation, you don't talk about simplifying a function. The point of interpolation is not to simplify. Someone lumped interpolation and approximation under one heading in a textbook and there you go...
Why specify the domain of a function that is already defined from minus infinity to plus infinity?
As mathematical gurus write textbooks - a dump of all in one chapter, so on these textbooks senior lecturers give lectures and the same dump goes to the heads of students, some of which later become teachers and the cycle closes. Then some of them, instead of explaining the meaning of established definitions, introduce new ones... instead of a function, it's a mapping and it's a dead end. Some are loaded with all this terminology and think that they became mathematicians... some kind of disease of leftism in communism.
A practical task, where I had to both define interpolation nodes ( function definition area) and simplify a function defined by an explicit formula: displaying part or all of an ellipse with slanted axes. The egavga.bgi driver had no commands to draw an ellipse with slanted axes on the screen. I had to replace the curve with pieces of circles, which were already being output at a normal speed. I think in modern screen output tools this is already done easier, hardware-wise. But back then... ...I had to do a lot of twisting. And the method known in descriptive geometry of replacing the ellipse with an oval of 4 pieces of circles gave too rough a picture, we made 8 pieces.
And your "original" ideas about students and docents are better answered than I am by the text quoted in Raymond M. Smallian's book "What's the name of this book?":
"There is a gap between the frontiers reached by modern mathematics and the traditionally 'established' mathematics courses that has been colourfully described by the remarkable representative of that science, the educator and populariser Hugo Steingauz: 'In mathematics, incomparably more clearly than in other disciplines, one feels the extent to which the march of all mankind has been extended. There are those of our contemporaries whose knowledge of mathematics dates back to an era older than the Egyptian pyramids, and they are in the great majority. Mathematical knowledge of a minor part of people has reached the Middle Ages, and the level of mathematics of XVIII century does not reach even one in a thousand... But the distance between those who are in the vanguard, and the boundless mass of travelers is growing, the procession is stretched, and walking in front of them distances more and more. They are out of sight, few are known, the stories about them are astonishing. There are those who simply do not believe in their existence.
P.S. One of the most popular threads of this forum (From Theory to Practice) is devoted to creation of a trading system, in particular by solving the Fokker-Planck integral differential equation. It is a special case (for Markovian processes) of Kolmogorov-Chepman equation where linear operators representing probability distribution functions are involved. These mappings are not functions at all, since the sets A and B contain distributions, not numbers.
Source: Wikipedia, the free encyclopedia.
The Kolmogorov-Chepman equation for the one-parameter family of continuous linear operators P(t), t>0 in topological vector space, expresses a semigroup property:
P (t+s) = P(t) P(s).
This term is most commonly used in the theory of homogeneous Markov random processes, where P(t), t>=0 is an operator that converts the probability distribution at the initial time to the probability distribution at time t (P(0) = 1).
I need to interpolate a function with arbitrary settings, so I chose splines.
I understand correctly that I will get different interpolants by the number of node points, what else can I vary?
And the second question, what is better to choose for interpolation from the list, if I just need to build many different interpolations of the original series (variation is important)?
If you need "variation", exact interpolation methods will not work for you, only ANC and the like.
As I understand from your subsequent posts, you want to use an interpolation method to solve the extrapolation problem. The only workable method is trend, everything else is rubbish.
Vladimir, I'm sorry. I'm just a slower thinker.
You know what I mean.
For a trader, extrapolation, not interpolation or approximation, is the most valuable.
Splines are not suitable for extrapolation.
I have great experience and understanding in polynomial approximation-extrapolation. Less experience - Fourier.
Extrapolation by polynomial and Fouriermethods are completely different in nature. Fourier extrapolation can be applied only to the flat market due to its periodic nature (this line is a sum of sinusoids of different frequency, phase and amplitude), and it always tends to go back,whereas polynomial extrapolation, on the contrary, is good for the trend, as it always tries to "fly up" or down due to its degree nature.
Therefore, it makes sense to combine these two methods for good extrapolation results.
The polynomial approximation is of particular interest for programmers because this type of approximation is very well optimized and can be calculated very quickly. I managed to get out of cycles for calculation of coefficients.
It is also important to remember that all types of approximation create redrawable lines with each new point. Only the tracer from the approximating line is not redrawn.
A polynomial approximation has only one solution as opposed to a Fourier approximation. This allows the creation of unique non redrawable slides:
Fourier is not suitable for extrapolation. There is nothing/no reason to extrapolate a periodic function: just take the values from the left edge - which is what you will theoretically get if the extrapolation error tends to zero, i.e. if you take all harmonics for the calculation, not the selected ones.
That is why its application to a flat gives a more plausible result - the presence of a narrow range of price fluctuations. Therefore, the extrapolation error is not crucial there (at the flat).
Fourier is not suitable for extrapolation. There is nothing/no reason to extrapolate a periodic function: just take the values from the left edge - which is what you will theoretically get if the extrapolation error tends to zero, i.e. if you take all harmonics for the calculation, not the selected ones.
That is why its application to a flat gives a more plausible result - the presence of a narrow range of price fluctuations. Therefore, the extrapolation error is not crucial there (at the flat).
I'm sorry, I cannot understand what you mean. Probably due to my limitation. But I tried.
But have a look and see this example:
https://www.mql5.com/ru/forum/216298/page5#comment_6484839