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How to find a non linear model that fits a set of coordinates
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I'm trying to find a function that satisfies the following coordinates:
$$(1, 1)$$$$(2, 0.84)$$$$(4, 1.5)$$$$(31, 4.1)$$$$(44, 5)$$
The x parameters are always discrete and the function doesn't need to be exact but as close as possible although the first three coordinates are the most important ones.
The function is not asymptotic.
The growth for large numbers should be really slow and should be configurable if possible.
It supposed to look like this:
What is the best method for finding this function?
I've tried to play a bit with desmos but I don't have a specific way to approach this problem.
functions logarithms nonlinear-system
asked Jul 15 at 9:35
Drxxd
1305
add a comment |Â
up vote
0
down vote
favorite
I'm trying to find a function that satisfies the following coordinates:
$$(1, 1)$$$$(2, 0.84)$$$$(4, 1.5)$$$$(31, 4.1)$$$$(44, 5)$$
The x parameters are always discrete and the function doesn't need to be exact but as close as possible although the first three coordinates are the most important ones.
The function is not asymptotic.
The growth for large numbers should be really slow and should be configurable if possible.
It supposed to look like this:
What is the best method for finding this function?
I've tried to play a bit with desmos but I don't have a specific way to approach this problem.
functions logarithms nonlinear-system
asked Jul 15 at 9:35
Drxxd
1305
1
You should give us information about the expected asymptotic behavior, i.e. orders of growth for small and for large values of $x$, based on physical arguments. Otherwise trying "any similar model" is cheap empiricism.
– Yves Daoust
Jul 15 at 9:44
You're right.. I need to think about that. I'll post a reply again when I edit the question
– Drxxd
Jul 15 at 9:55
"asymptomatic" ???
– Yves Daoust
Jul 15 at 14:22
@YvesDaoust lol, I copied it from the answer.
– Drxxd
Jul 15 at 14:29
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I'm trying to find a function that satisfies the following coordinates:
$$(1, 1)$$$$(2, 0.84)$$$$(4, 1.5)$$$$(31, 4.1)$$$$(44, 5)$$
The x parameters are always discrete and the function doesn't need to be exact but as close as possible although the first three coordinates are the most important ones.
The function is not asymptotic.
The growth for large numbers should be really slow and should be configurable if possible.
It supposed to look like this:
What is the best method for finding this function?
I've tried to play a bit with desmos but I don't have a specific way to approach this problem.
functions logarithms nonlinear-system
asked Jul 15 at 9:35
Drxxd
1305
I'm trying to find a function that satisfies the following coordinates:
$$(1, 1)$$$$(2, 0.84)$$$$(4, 1.5)$$$$(31, 4.1)$$$$(44, 5)$$
The x parameters are always discrete and the function doesn't need to be exact but as close as possible although the first three coordinates are the most important ones.
The function is not asymptotic.
The growth for large numbers should be really slow and should be configurable if possible.
It supposed to look like this:
What is the best method for finding this function?
I've tried to play a bit with desmos but I don't have a specific way to approach this problem.
functions logarithms nonlinear-system
asked Jul 15 at 9:35
Drxxd
1305
edited Jul 15 at 14:29
asked Jul 15 at 9:35
Drxxd
1305
asked Jul 15 at 9:35
Drxxd
1305
asked Jul 15 at 9:35
Drxxd
1305
1305
1
You should give us information about the expected asymptotic behavior, i.e. orders of growth for small and for large values of $x$, based on physical arguments. Otherwise trying "any similar model" is cheap empiricism.
– Yves Daoust
Jul 15 at 9:44
You're right.. I need to think about that. I'll post a reply again when I edit the question
– Drxxd
Jul 15 at 9:55
"asymptomatic" ???
– Yves Daoust
Jul 15 at 14:22
@YvesDaoust lol, I copied it from the answer.
– Drxxd
Jul 15 at 14:29
add a comment |Â
1
You should give us information about the expected asymptotic behavior, i.e. orders of growth for small and for large values of $x$, based on physical arguments. Otherwise trying "any similar model" is cheap empiricism.
– Yves Daoust
Jul 15 at 9:44
You're right.. I need to think about that. I'll post a reply again when I edit the question
– Drxxd
Jul 15 at 9:55
"asymptomatic" ???
– Yves Daoust
Jul 15 at 14:22
@YvesDaoust lol, I copied it from the answer.
– Drxxd
Jul 15 at 14:29
1
1
You should give us information about the expected asymptotic behavior, i.e. orders of growth for small and for large values of $x$, based on physical arguments. Otherwise trying "any similar model" is cheap empiricism.
– Yves Daoust
Jul 15 at 9:44
You should give us information about the expected asymptotic behavior, i.e. orders of growth for small and for large values of $x$, based on physical arguments. Otherwise trying "any similar model" is cheap empiricism.
– Yves Daoust
Jul 15 at 9:44
You're right.. I need to think about that. I'll post a reply again when I edit the question
– Drxxd
Jul 15 at 9:55
You're right.. I need to think about that. I'll post a reply again when I edit the question
– Drxxd
Jul 15 at 9:55
"asymptomatic" ???
– Yves Daoust
Jul 15 at 14:22
"asymptomatic" ???
– Yves Daoust
Jul 15 at 14:22
@YvesDaoust lol, I copied it from the answer.
– Drxxd
Jul 15 at 14:29
@YvesDaoust lol, I copied it from the answer.
– Drxxd
Jul 15 at 14:29
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
1
down vote
Without more information I can't find the best solution (need information about minimum value, behavior as the function approaches infinity, whether it is asymptotic or not), but your graph seems like it is not asymptomatic as $xtoinfty$, and it seems like the function
$$ f(x) = frac3x^3/24sqrtx^2-1 $$
Fits quite well.
answered Jul 15 at 10:35
user496634
19518
Two things, First of all, what was your approach of finding this function, secondly the first coordinates (1,1) and (2,0.84) are more important
– Drxxd
Jul 15 at 10:54
@Drxxd since the data points aren't asymptotic as $x$ goes to infinity, a good guess will be that of the graph $sqrtx$. But then it goes to infinity rapidly as $x$ goes to zero, so we want to multiply by something along the lines of $1/x$, but we want the function to go to one as it goes to infinity, so something like $1/sqrt1-1/x^2$ works. Then we are left with the constant term which can be found by just testing different values.
– user496634
Jul 15 at 10:59
@Drxxd If you value the first two data points more, just decrease the constant term. U might also consider raising the power of the $sqrtx$ term (say $x^0.6$).
– user496634
Jul 15 at 11:01
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
Without more information I can't find the best solution (need information about minimum value, behavior as the function approaches infinity, whether it is asymptotic or not), but your graph seems like it is not asymptomatic as $xtoinfty$, and it seems like the function
$$ f(x) = frac3x^3/24sqrtx^2-1 $$
Fits quite well.
answered Jul 15 at 10:35
user496634
19518
Two things, First of all, what was your approach of finding this function, secondly the first coordinates (1,1) and (2,0.84) are more important
– Drxxd
Jul 15 at 10:54
@Drxxd since the data points aren't asymptotic as $x$ goes to infinity, a good guess will be that of the graph $sqrtx$. But then it goes to infinity rapidly as $x$ goes to zero, so we want to multiply by something along the lines of $1/x$, but we want the function to go to one as it goes to infinity, so something like $1/sqrt1-1/x^2$ works. Then we are left with the constant term which can be found by just testing different values.
– user496634
Jul 15 at 10:59
@Drxxd If you value the first two data points more, just decrease the constant term. U might also consider raising the power of the $sqrtx$ term (say $x^0.6$).
– user496634
Jul 15 at 11:01
add a comment |Â
up vote
1
down vote
Without more information I can't find the best solution (need information about minimum value, behavior as the function approaches infinity, whether it is asymptotic or not), but your graph seems like it is not asymptomatic as $xtoinfty$, and it seems like the function
$$ f(x) = frac3x^3/24sqrtx^2-1 $$
Fits quite well.
answered Jul 15 at 10:35
user496634
19518
Two things, First of all, what was your approach of finding this function, secondly the first coordinates (1,1) and (2,0.84) are more important
– Drxxd
Jul 15 at 10:54
@Drxxd since the data points aren't asymptotic as $x$ goes to infinity, a good guess will be that of the graph $sqrtx$. But then it goes to infinity rapidly as $x$ goes to zero, so we want to multiply by something along the lines of $1/x$, but we want the function to go to one as it goes to infinity, so something like $1/sqrt1-1/x^2$ works. Then we are left with the constant term which can be found by just testing different values.
– user496634
Jul 15 at 10:59
@Drxxd If you value the first two data points more, just decrease the constant term. U might also consider raising the power of the $sqrtx$ term (say $x^0.6$).
– user496634
Jul 15 at 11:01
add a comment |Â
up vote
1
down vote
up vote
1
down vote
Without more information I can't find the best solution (need information about minimum value, behavior as the function approaches infinity, whether it is asymptotic or not), but your graph seems like it is not asymptomatic as $xtoinfty$, and it seems like the function
$$ f(x) = frac3x^3/24sqrtx^2-1 $$
Fits quite well.
answered Jul 15 at 10:35
user496634
19518
Without more information I can't find the best solution (need information about minimum value, behavior as the function approaches infinity, whether it is asymptotic or not), but your graph seems like it is not asymptomatic as $xtoinfty$, and it seems like the function
$$ f(x) = frac3x^3/24sqrtx^2-1 $$
Fits quite well.
answered Jul 15 at 10:35
user496634
19518
answered Jul 15 at 10:35
user496634
19518
answered Jul 15 at 10:35
user496634
19518
answered Jul 15 at 10:35
user496634
19518
19518
Two things, First of all, what was your approach of finding this function, secondly the first coordinates (1,1) and (2,0.84) are more important
– Drxxd
Jul 15 at 10:54
@Drxxd since the data points aren't asymptotic as $x$ goes to infinity, a good guess will be that of the graph $sqrtx$. But then it goes to infinity rapidly as $x$ goes to zero, so we want to multiply by something along the lines of $1/x$, but we want the function to go to one as it goes to infinity, so something like $1/sqrt1-1/x^2$ works. Then we are left with the constant term which can be found by just testing different values.
– user496634
Jul 15 at 10:59
@Drxxd If you value the first two data points more, just decrease the constant term. U might also consider raising the power of the $sqrtx$ term (say $x^0.6$).
– user496634
Jul 15 at 11:01
add a comment |Â
Two things, First of all, what was your approach of finding this function, secondly the first coordinates (1,1) and (2,0.84) are more important
– Drxxd
Jul 15 at 10:54
@Drxxd since the data points aren't asymptotic as $x$ goes to infinity, a good guess will be that of the graph $sqrtx$. But then it goes to infinity rapidly as $x$ goes to zero, so we want to multiply by something along the lines of $1/x$, but we want the function to go to one as it goes to infinity, so something like $1/sqrt1-1/x^2$ works. Then we are left with the constant term which can be found by just testing different values.
– user496634
Jul 15 at 10:59
@Drxxd If you value the first two data points more, just decrease the constant term. U might also consider raising the power of the $sqrtx$ term (say $x^0.6$).
– user496634
Jul 15 at 11:01
Two things, First of all, what was your approach of finding this function, secondly the first coordinates (1,1) and (2,0.84) are more important
– Drxxd
Jul 15 at 10:54
Two things, First of all, what was your approach of finding this function, secondly the first coordinates (1,1) and (2,0.84) are more important
– Drxxd
Jul 15 at 10:54
@Drxxd since the data points aren't asymptotic as $x$ goes to infinity, a good guess will be that of the graph $sqrtx$. But then it goes to infinity rapidly as $x$ goes to zero, so we want to multiply by something along the lines of $1/x$, but we want the function to go to one as it goes to infinity, so something like $1/sqrt1-1/x^2$ works. Then we are left with the constant term which can be found by just testing different values.
– user496634
Jul 15 at 10:59
@Drxxd since the data points aren't asymptotic as $x$ goes to infinity, a good guess will be that of the graph $sqrtx$. But then it goes to infinity rapidly as $x$ goes to zero, so we want to multiply by something along the lines of $1/x$, but we want the function to go to one as it goes to infinity, so something like $1/sqrt1-1/x^2$ works. Then we are left with the constant term which can be found by just testing different values.
– user496634
Jul 15 at 10:59
@Drxxd If you value the first two data points more, just decrease the constant term. U might also consider raising the power of the $sqrtx$ term (say $x^0.6$).
– user496634
Jul 15 at 11:01
@Drxxd If you value the first two data points more, just decrease the constant term. U might also consider raising the power of the $sqrtx$ term (say $x^0.6$).
– user496634
Jul 15 at 11:01
add a comment |Â
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1
You should give us information about the expected asymptotic behavior, i.e. orders of growth for small and for large values of $x$, based on physical arguments. Otherwise trying "any similar model" is cheap empiricism.
– Yves Daoust
Jul 15 at 9:44
You're right.. I need to think about that. I'll post a reply again when I edit the question
– Drxxd
Jul 15 at 9:55
"asymptomatic" ???
– Yves Daoust
Jul 15 at 14:22
@YvesDaoust lol, I copied it from the answer.
– Drxxd
Jul 15 at 14:29