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 Tkipp July 3rd, 2017 04:52 PM

Publishers

Hello,

I recently fine-tuned a mathematical method that creates representations of the integrals of power functions with a tight degree of accuracy around 1% off of the real value at the point of max deviation. I had three questions that you would hopefully be able to answer for me:

1.) Do you believe that this would be significant enough of a finding to get published?

2.) If yes, where should I submit it to? I unfortunately finished it a year after finishing college, but I started working on it in my freshman year.

3.) Where would I get a detailed review of the work? (I am pretty sure many people would rather not read a 50 page paper on a method that may or may not be significant.)

 Joppy July 4th, 2017 07:06 PM

A quadrature method for approximating power functions?

 Tkipp July 5th, 2017 03:22 PM

Quote:
 Originally Posted by Joppy (Post 574651) A quadrature method for approximating power functions?
Nope, what it is, is what I call a mirror function. A mirror function is a function that behaves exactly like or nearly like the function it is based off of. A simple example of this is:

((x-5)/2)-(sqrt(x^2)/2)+(7/2) which is a mirror of 1.

It is pretty much a simple form of Calculus of Variations. https://en.wikipedia.org/wiki/Calculus_of_variations

 Maschke July 5th, 2017 04:56 PM

Quote:
 Originally Posted by Tkipp (Post 574751) ((x-5)/2)-(sqrt(x^2)/2)+(7/2) which is a mirror of 1.
sqrt(x^2). Is this intended as a joke? Like an obfuscated code contest but for math?

 Tkipp July 5th, 2017 05:07 PM

Quote:
 Originally Posted by Maschke (Post 574757) sqrt(x^2). Is this intended as a joke? Like an obfuscated code contest but for math?
I did say simple example didn't I?
I am just showing simple functions can be put together to represent anything from something as simple as a constant such as 1 or as complex as the integral of a power function.

 Micrm@ss July 16th, 2017 02:27 PM

Do you mean integrals like $\int x^p dx$? Sorry if I fail to understand, but don't we already know exactly what these integrals are?

 Tkipp July 17th, 2017 03:56 PM

Quote:
 Originally Posted by Micrm@ss (Post 575438) Do you mean integrals like $\int x^p dx$? Sorry if I fail to understand, but don't we already know exactly what these integrals are?
Yep, except it is for functions like exp(x^2), x^x, etc, which currently do not have such a representation.

 Micrm@ss July 17th, 2017 04:01 PM

Quote:
 Originally Posted by Tkipp (Post 575490) Yep, except for functions like exp(x^2), x^x, etc.
OK nice. It has been rigorously proven that these integrals cannot be found analytically in terms of elementary functions.

However, we do already know how to approximate these integrals to any degree of accuracy. So if you want to publish this, then you'll need to show somehow that your method is better than the currently known ones. Better could mean that it is more numerically stable, or it is faster, or...

If you could show this, then yes, people would be very interested in this result. You don't even have to show it mathematically, doing a simulation study where your technique beats the competition would already be quite good!

 Tkipp July 17th, 2017 04:45 PM

https://i.stack.imgur.com/ABLLu.png

https://i.stack.imgur.com/QctML.png

Here is a run I took with exp(x^2). The first is the integral values, the second the derivative of my function divided by exp(x^2) minus 1. As you can see it is fairly accurate, and these graphs capture the max error deviation, which is centered around x=1, -1. As the approaches both positive and negative infinity the error ratio goes to zero.

 Micrm@ss July 17th, 2017 04:49 PM

Quote:
 Originally Posted by Tkipp (Post 575492) https://i.stack.imgur.com/ABLLu.png https://i.stack.imgur.com/QctML.png Here is a run I took with exp(x^2). The first is the integral values, the second the derivative of my function divided by exp(x^2) minus 1. As you can see it is fairly accurate, and these graphs capture the max error deviation, which is centered around x=1, -1. As the approaches both positive and negative infinity the error ratio goes to zero.
This is not accurate at all. It should give the same value as the standard methods. You might say the error is small, but in a large program, such small errors will compound quickly.

So if your method doesn't give the correct answer, what is its benefit? Is it faster? More stable?

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