Interpolation, approximation and the like (alglib package) - page 3
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What hasn't anyone solved? The problem of interpolating a function? The problem of interpolating a function - no one has solved such a problem and no one ever will.
Do you want me to solve it for you? Pick any simple function. And you will learn how to do it yourself.
What hasn't anyone solved? The problem of interpolating a function? The problem of interpolation of a function - no one has solved such a problem and no one ever will.
I don't believe it. What are you talking about? https://poznayka.org/s91750t1.html
I can't believe my eyes. What do you mean? https://poznayka.org/s91750t1.html
What is this "cognitive", a website for schoolchildren and pensioners, under the slogan "to teach what not to teach"? A very authoritative source.
Give me a definition of the term "interpolation of a function".
I know these definitions:
Interpolation is a way of finding intermediate values of a quantity from an available discrete set of known values
Approximation (from Latin proxima - the nearest) or approximation - a scientific method consisting in replacement of some objects by others, which are in some sense close to the original, but simpler.
And what "interpolation of a function" is, I have no idea.
How about "function interpolation"?Do you want me to solve it for you? Pick a simple function. You'll learn how to do it yourself.
y=x^2, make it even simpler: y=2*x
What is this "cognitive", a website for schoolchildren and pensioners, under the slogan "teach what not to teach"? A very authoritative source.
Give me a definition of the term "interpolation of a function".
I know these definitions:
Interpolation is a way of finding intermediate values of a quantity from an available discrete set of known values
Approximation (from Latin proxima - nearest) or approximation - a scientific method consisting in replacement of some objects by others, which are in some sense close to the original, but simpler.
And what "interpolation of a function" is, I have no idea.
Can "interpolation bea function"?You have correctly named what interpolation is. Decipher what "values of a quantity at intermediate points where it is not given" is. It is a rule that maps x values to y values. That is, a function. And it's a rule that we try to set as closely as possible to the "original" function. For example, so that the curve representing the "original" has no kinks (jumps in the first derivative). And often we assume that the original was a simple broken line, and do sliding interpolation by straight line segments.
If you don't want to "cognate", here's a website to help studentshttps://www.matburo.ru/ex_cm.php?p1=cmip:
Numerical Methods:
Interpolation of Functions
Problem solving: Interpolation of table-defined functions
This section contains examples of solved problems on the topic of interpolation of functions given tabularly.
End of quotation.
Or a completely authoritative source. Do you trust Samarsky? Here is the beginning of the table of contents of the problem book "Samarsky Alexander Andreevich, Vabishchevich Peter Nikolaevich, Samarsky Elena Aleksandrovna
Problems and exercises in numerical methods: Textbook. - Moscow: Editorial URSS, 2000. - 208 p.":
Chapter 1: Interpolation and Approximation of Functions........................................... 8
1.1 Tasks of interpolation and approximation of functions ........................................ 8
1.2 Algorithms for interpolation and approximation of functions ............................... 10
1.2.1 Polynomial interpolation......................................................... 10
1.2.2. Interpolation s ppl .............................................................. 11
1.2.3 Approximation of functions in normalized space .... 12
1.3. Appearances ........................................................................................................... 13
1.4 Hints ....................................................................................................................... 18
I will say for myself where the problems of interpolation of tabularly given functions come from. From the high price of each "given" point. For example, to get one, you have to drill a well to a depth of 5k. Or the value at a given point is calculated on a computer, but in 3 hours (or 30 thousand hours), by summing up a slowly-slowly converging series. Sometimes there is no data other than the given points and there cannot be.
In this case, the accuracy (error) of the value at a point is limited, and there is no point in chasing an exact match of the value calculated by the replacement rule with this point. It is better to replace the interpolation problem with the approximation problem with control of acceptable error of replacement.
y=x^2, let's make it even simpler: y=2*x
I'll go through the libs, van moment. And I'll do it tonight.
As you've written above, here's more http://matlab.exponenta.ru/spline/book1/10.php
You have correctly stated what interpolation is. Decipher what "values of a quantity at intermediate points where it is not given" is. It is a rule that maps x values to y values. That is, a function. And it's a rule that we try to set as closely as possible to the "original" function. For example, so that the curve representing the "original" has no kinks (jumps in the first derivative). And often we assume that the original was a simple broken line, and do sliding interpolation by straight line segments.
If you don't want to "cognate", here's a website to help studentshttps://www.matburo.ru/ex_cm.php?p1=cmip:
Numerical Methods:
Interpolation of Functions
Problem solving: Interpolation of table-defined functions
This section contains examples of solved problems on the topic of interpolation of tabularly defined functions.
End of quotation.
Or a completely authoritative source. Do you trust Samarsky? Here is the beginning of the table of contents of the problem book "Samarsky Alexander Andreevich, Vabishchevich Pyotr Nikolaevich, Samarsky Elena Aleksandrovna
Problems and exercises in numerical methods: Textbook. - Moscow: Editorial URSS, 2000. - 208 p.":
Chapter 1: Interpolation and Approximation of Functions........................................... 8
1.1 Tasks of interpolation and approximation of functions ........................................ 8
1.2 Algorithms for interpolation and approximation of functions ............................... 10
1.2.1 Polynomial interpolation......................................................... 10
1.2.2. Interpolation s ppl .............................................................. 11
1.2.3 Approximation of functions in normalized space .... 12
1.3. Appearances ........................................................................................................... 13
1.4 Hints ....................................................................................................................... 18
I will say for myself where the problems of interpolation of tabularly given functions come from. From the high price of each "given" point. For example, you have to drill a well to a depth of 5k to get one. Or the value at a given point is calculated on a computer, but in 3 hours (or 30 thousand hours), by summing up a slowly-slowly converging series. Sometimes there is no data other than the given points and there cannot be.
In this case, the accuracy (error) of the value at a point is limited, and there is no point in chasing for an exact match of the value calculated by the substituting rule with this point. The interpolation problem should better be replaced by the approximation problem with control over the acceptable error of substitution.
In the above quote, one word is highlighted in red. This is the function that interpolates, but it interpolates a tabulated function (i.e. a series of data). Which function is more appropriate to call, a tabulated function (data series), or a mathematical formula like y=k*x, y=x^2? I think the latter is the mathematical one. So an expression like "interpolation of a function" looks wild.
And here's the reason, I guess - the title in a reputable book: "Interpolation and Approximation of Functions". Here the word "functions" refers to "approximation" and the word "interpolation" itself. Someone split the title and got two titles "interpolation of functions" and "approximation of functions".
Approximation of functions, i.e. approximation of functions, is OK. They take a mathematical function, select its coefficients and thus approximate to the tabulated data.
I'll go through the libs, van moment. I'll do it tonight.
You said it above, here's more http://matlab.exponenta.ru/spline/book1/10.php.
No, you won't. Interpolation requires a series of data, not a mathematical function. If a mathematical function is given, then there is nothing to interpolate and there is no point in interpolation.
Dear Maxim,
If I am not wrong, then by using splines you are trying to feed the Mt5 screen price data in discrete packets to a neural network in which each segment or packet of price data will represent a separate function by itself and then, the neural network will choose the best function automatically for a specific price segment based on least mean square error (MSE) of past trained data. Am I correct in my understanding?
I mean you are trying a similar approach of game theory of feeding pixels to a game and in your case, you are trying to feed the price in the form of splines. Is that correct?
Thanks...
You won't. Interpolation requires a range of data, not a mathematical function. If a mathematical function is given, there is nothing to interpolate and there is no point in interpolation.
Well, discrete points are selected, of course. And you can do it on an irregular grid. That is why interpolation is convenient for transforming a series.