The multiplier between 0.0 to 1.0 that cause 2 points collapse the fastest
$begingroup$
I don't know what kind this problem is.
May be it is similar as finding energy loss coefficient k in every turn in a spring motion simulation that has the shortest time to become stable?
I have two points $x_1$ $x_2$ (represented by real number). They are separated by a distance $d$. They have an acceleration $a=d$, pointing to each other.
That is: $v_1$ $v_2$(velocities) $a_1$ $a_2$(acceleration) initially = 0
In the following iteration:
Step 1: $a_1=x_2-x_1;$ $a_2=x_1-x_2$
Step 2: $v_1=v_1+a_1;$ $v_2=v_2+a_2$
Step 3: $x_1=x_1+v_1;$ $x_2=x_2+v_2$
Step 4: $v_1=v_1times k;$ $v_2=v_2times k$, where k is a constant from 0 to 1
Step 5: Go to Step 1
I am wondering, what is the constant $k$ that can collapse 2 points together in the least iterations. That is, the 2 points are very close together and very stable (low velocity).
I know that $k$ can not be too close to 0 or 1. At first, I guess it may be 0.5. However in my test, it is not, nor 0.25. The value seems to be a strange decimals around 0.17 to 0.18. I notice that is close to $1over2e$. I don't know if it is.
I want to know why, and want to know are there some studies similiar to this kind of problem?
After some programming and test, I find that $k$ is around 0.171578 and 0.17579. Is there an exact number represent it?
sequences-and-series approximation rate-of-convergence convergence-acceleration
asked Dec 19 '18 at 18:04
Min ChanMin Chan
63
$endgroup$
add a comment |
$begingroup$
I don't know what kind this problem is.
May be it is similar as finding energy loss coefficient k in every turn in a spring motion simulation that has the shortest time to become stable?
I have two points $x_1$ $x_2$ (represented by real number). They are separated by a distance $d$. They have an acceleration $a=d$, pointing to each other.
That is: $v_1$ $v_2$(velocities) $a_1$ $a_2$(acceleration) initially = 0
In the following iteration:
Step 1: $a_1=x_2-x_1;$ $a_2=x_1-x_2$
Step 2: $v_1=v_1+a_1;$ $v_2=v_2+a_2$
Step 3: $x_1=x_1+v_1;$ $x_2=x_2+v_2$
Step 4: $v_1=v_1times k;$ $v_2=v_2times k$, where k is a constant from 0 to 1
Step 5: Go to Step 1
I am wondering, what is the constant $k$ that can collapse 2 points together in the least iterations. That is, the 2 points are very close together and very stable (low velocity).
I know that $k$ can not be too close to 0 or 1. At first, I guess it may be 0.5. However in my test, it is not, nor 0.25. The value seems to be a strange decimals around 0.17 to 0.18. I notice that is close to $1over2e$. I don't know if it is.
I want to know why, and want to know are there some studies similiar to this kind of problem?
After some programming and test, I find that $k$ is around 0.171578 and 0.17579. Is there an exact number represent it?
sequences-and-series approximation rate-of-convergence convergence-acceleration
asked Dec 19 '18 at 18:04
Min ChanMin Chan
63
$endgroup$
add a comment |
$begingroup$
I don't know what kind this problem is.
May be it is similar as finding energy loss coefficient k in every turn in a spring motion simulation that has the shortest time to become stable?
I have two points $x_1$ $x_2$ (represented by real number). They are separated by a distance $d$. They have an acceleration $a=d$, pointing to each other.
That is: $v_1$ $v_2$(velocities) $a_1$ $a_2$(acceleration) initially = 0
In the following iteration:
Step 1: $a_1=x_2-x_1;$ $a_2=x_1-x_2$
Step 2: $v_1=v_1+a_1;$ $v_2=v_2+a_2$
Step 3: $x_1=x_1+v_1;$ $x_2=x_2+v_2$
Step 4: $v_1=v_1times k;$ $v_2=v_2times k$, where k is a constant from 0 to 1
Step 5: Go to Step 1
I am wondering, what is the constant $k$ that can collapse 2 points together in the least iterations. That is, the 2 points are very close together and very stable (low velocity).
I know that $k$ can not be too close to 0 or 1. At first, I guess it may be 0.5. However in my test, it is not, nor 0.25. The value seems to be a strange decimals around 0.17 to 0.18. I notice that is close to $1over2e$. I don't know if it is.
I want to know why, and want to know are there some studies similiar to this kind of problem?
After some programming and test, I find that $k$ is around 0.171578 and 0.17579. Is there an exact number represent it?
sequences-and-series approximation rate-of-convergence convergence-acceleration
asked Dec 19 '18 at 18:04
Min ChanMin Chan
63
$endgroup$
I don't know what kind this problem is.
May be it is similar as finding energy loss coefficient k in every turn in a spring motion simulation that has the shortest time to become stable?
I have two points $x_1$ $x_2$ (represented by real number). They are separated by a distance $d$. They have an acceleration $a=d$, pointing to each other.
That is: $v_1$ $v_2$(velocities) $a_1$ $a_2$(acceleration) initially = 0
In the following iteration:
Step 1: $a_1=x_2-x_1;$ $a_2=x_1-x_2$
Step 2: $v_1=v_1+a_1;$ $v_2=v_2+a_2$
Step 3: $x_1=x_1+v_1;$ $x_2=x_2+v_2$
Step 4: $v_1=v_1times k;$ $v_2=v_2times k$, where k is a constant from 0 to 1
Step 5: Go to Step 1
I am wondering, what is the constant $k$ that can collapse 2 points together in the least iterations. That is, the 2 points are very close together and very stable (low velocity).
I know that $k$ can not be too close to 0 or 1. At first, I guess it may be 0.5. However in my test, it is not, nor 0.25. The value seems to be a strange decimals around 0.17 to 0.18. I notice that is close to $1over2e$. I don't know if it is.
I want to know why, and want to know are there some studies similiar to this kind of problem?
After some programming and test, I find that $k$ is around 0.171578 and 0.17579. Is there an exact number represent it?
sequences-and-series approximation rate-of-convergence convergence-acceleration
sequences-and-series approximation rate-of-convergence convergence-acceleration
asked Dec 19 '18 at 18:04
Min ChanMin Chan
63
asked Dec 19 '18 at 18:04
Min ChanMin Chan
63
edited Dec 20 '18 at 6:52
Min Chan
asked Dec 19 '18 at 18:04
Min ChanMin Chan
63
asked Dec 19 '18 at 18:04
Min ChanMin Chan
63
asked Dec 19 '18 at 18:04
Min ChanMin Chan
63
63
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