Choosing functions for data approximation with least square method
$begingroup$
I have data (supposedly a volt-amper characteristic of some TTL component) which is:
U[V]: x := [ 0.25, 1.0, 1.4, 1.45, 1.50, 1.55, 1.6, 5.0]
I[mA]: y := [-0.85, -0.65, -0.54, -0.31, -0.1, -0.02, 0.0, 0.004]
I'd like to approximate this data using the least squares method, so that I can after get a "reasonably accurate" values for 0.8V and 3.5V. The approximated function should however be "reasonably well approximated" for other values too. The best accuracy for me wasn't even $ epsilon = 0.1 $ (the error was something like 0.28),so anything beyond that is progress.
What I need is the functions, which will help me approximate this data. Getting the c-values (the multipliers for the functions) does not concern me, as I have a function that computes these sort-of optimally.
I've had some success trying to use these functions, but haven't been able to fit it properly and honestly I am out of ideas.
$$
f_{1} := -e^{-t^2} \
f_{2} := -frac{1}{t+1} \
f_{3} := 1
$$
I would welcome any kind of help, I am struggling with even finding a function that would look at least something like this.
numerical-methods approximation
edited Jan 10 at 11:10
Mefitico
1,184218
asked Jan 9 at 18:12
WelsyWelsy
1
$endgroup$
add a comment |
$begingroup$
I have data (supposedly a volt-amper characteristic of some TTL component) which is:
U[V]: x := [ 0.25, 1.0, 1.4, 1.45, 1.50, 1.55, 1.6, 5.0]
I[mA]: y := [-0.85, -0.65, -0.54, -0.31, -0.1, -0.02, 0.0, 0.004]
I'd like to approximate this data using the least squares method, so that I can after get a "reasonably accurate" values for 0.8V and 3.5V. The approximated function should however be "reasonably well approximated" for other values too. The best accuracy for me wasn't even $ epsilon = 0.1 $ (the error was something like 0.28),so anything beyond that is progress.
What I need is the functions, which will help me approximate this data. Getting the c-values (the multipliers for the functions) does not concern me, as I have a function that computes these sort-of optimally.
I've had some success trying to use these functions, but haven't been able to fit it properly and honestly I am out of ideas.
$$
f_{1} := -e^{-t^2} \
f_{2} := -frac{1}{t+1} \
f_{3} := 1
$$
I would welcome any kind of help, I am struggling with even finding a function that would look at least something like this.
numerical-methods approximation
edited Jan 10 at 11:10
Mefitico
1,184218
asked Jan 9 at 18:12
WelsyWelsy
1
$endgroup$
$begingroup$
Do you have any reference on what curve to expect from this component? Usually there should be some function with few parameters that models the behavior fairly well and have parameters you can estimate with your available data. If this is a practical problem and you do need some kind of quick interpolation, you could consider using a spline which would fit the points exactly with some smoothness properties that makes them better than linear interpolation between two points..
$endgroup$
– Mefitico
Jan 9 at 18:19
$begingroup$
This is an excercise for my course "Numerical methods", which requires me to use the least square methods functions provided to me. Sadly, the excercise only states: "Find a reasonable approximation of this data, using this approximation, estimate the differential entry resistance with entry voltage 0.8V and 3.5V. That's all there is.
$endgroup$
– Welsy
Jan 9 at 18:24
$begingroup$
Did you simply try polynoms ?
$endgroup$
– Damien
Jan 9 at 18:28
$begingroup$
I've tried using basic polynoms from t to t^5 but I don't really know how to choose them well enough to get somewhere. When I use polynoms from degree 1 to 8, I get accuracy alright, but it doesn't look legit, you know what I mean... i.imgur.com/oaomaga.png
$endgroup$
– Welsy
Jan 9 at 18:34
add a comment |
$begingroup$
I have data (supposedly a volt-amper characteristic of some TTL component) which is:
U[V]: x := [ 0.25, 1.0, 1.4, 1.45, 1.50, 1.55, 1.6, 5.0]
I[mA]: y := [-0.85, -0.65, -0.54, -0.31, -0.1, -0.02, 0.0, 0.004]
I'd like to approximate this data using the least squares method, so that I can after get a "reasonably accurate" values for 0.8V and 3.5V. The approximated function should however be "reasonably well approximated" for other values too. The best accuracy for me wasn't even $ epsilon = 0.1 $ (the error was something like 0.28),so anything beyond that is progress.
What I need is the functions, which will help me approximate this data. Getting the c-values (the multipliers for the functions) does not concern me, as I have a function that computes these sort-of optimally.
I've had some success trying to use these functions, but haven't been able to fit it properly and honestly I am out of ideas.
$$
f_{1} := -e^{-t^2} \
f_{2} := -frac{1}{t+1} \
f_{3} := 1
$$
I would welcome any kind of help, I am struggling with even finding a function that would look at least something like this.
numerical-methods approximation
edited Jan 10 at 11:10
Mefitico
1,184218
asked Jan 9 at 18:12
WelsyWelsy
1
$endgroup$
I have data (supposedly a volt-amper characteristic of some TTL component) which is:
U[V]: x := [ 0.25, 1.0, 1.4, 1.45, 1.50, 1.55, 1.6, 5.0]
I[mA]: y := [-0.85, -0.65, -0.54, -0.31, -0.1, -0.02, 0.0, 0.004]
I'd like to approximate this data using the least squares method, so that I can after get a "reasonably accurate" values for 0.8V and 3.5V. The approximated function should however be "reasonably well approximated" for other values too. The best accuracy for me wasn't even $ epsilon = 0.1 $ (the error was something like 0.28),so anything beyond that is progress.
What I need is the functions, which will help me approximate this data. Getting the c-values (the multipliers for the functions) does not concern me, as I have a function that computes these sort-of optimally.
I've had some success trying to use these functions, but haven't been able to fit it properly and honestly I am out of ideas.
$$
f_{1} := -e^{-t^2} \
f_{2} := -frac{1}{t+1} \
f_{3} := 1
$$
I would welcome any kind of help, I am struggling with even finding a function that would look at least something like this.
numerical-methods approximation
numerical-methods approximation
edited Jan 10 at 11:10
Mefitico
1,184218
asked Jan 9 at 18:12
WelsyWelsy
1
edited Jan 10 at 11:10
Mefitico
1,184218
asked Jan 9 at 18:12
WelsyWelsy
1
edited Jan 10 at 11:10
Mefitico
1,184218
edited Jan 10 at 11:10
Mefitico
1,184218
edited Jan 10 at 11:10
Mefitico
1,184218
1,184218
asked Jan 9 at 18:12
WelsyWelsy
1
asked Jan 9 at 18:12
WelsyWelsy
1
asked Jan 9 at 18:12
WelsyWelsy
1
1
$begingroup$
Do you have any reference on what curve to expect from this component? Usually there should be some function with few parameters that models the behavior fairly well and have parameters you can estimate with your available data. If this is a practical problem and you do need some kind of quick interpolation, you could consider using a spline which would fit the points exactly with some smoothness properties that makes them better than linear interpolation between two points..
$endgroup$
– Mefitico
Jan 9 at 18:19
$begingroup$
This is an excercise for my course "Numerical methods", which requires me to use the least square methods functions provided to me. Sadly, the excercise only states: "Find a reasonable approximation of this data, using this approximation, estimate the differential entry resistance with entry voltage 0.8V and 3.5V. That's all there is.
$endgroup$
– Welsy
Jan 9 at 18:24
$begingroup$
Did you simply try polynoms ?
$endgroup$
– Damien
Jan 9 at 18:28
$begingroup$
I've tried using basic polynoms from t to t^5 but I don't really know how to choose them well enough to get somewhere. When I use polynoms from degree 1 to 8, I get accuracy alright, but it doesn't look legit, you know what I mean... i.imgur.com/oaomaga.png
$endgroup$
– Welsy
Jan 9 at 18:34
add a comment |
$begingroup$
Do you have any reference on what curve to expect from this component? Usually there should be some function with few parameters that models the behavior fairly well and have parameters you can estimate with your available data. If this is a practical problem and you do need some kind of quick interpolation, you could consider using a spline which would fit the points exactly with some smoothness properties that makes them better than linear interpolation between two points..
$endgroup$
– Mefitico
Jan 9 at 18:19
$begingroup$
This is an excercise for my course "Numerical methods", which requires me to use the least square methods functions provided to me. Sadly, the excercise only states: "Find a reasonable approximation of this data, using this approximation, estimate the differential entry resistance with entry voltage 0.8V and 3.5V. That's all there is.
$endgroup$
– Welsy
Jan 9 at 18:24
$begingroup$
Did you simply try polynoms ?
$endgroup$
– Damien
Jan 9 at 18:28
$begingroup$
I've tried using basic polynoms from t to t^5 but I don't really know how to choose them well enough to get somewhere. When I use polynoms from degree 1 to 8, I get accuracy alright, but it doesn't look legit, you know what I mean... i.imgur.com/oaomaga.png
$endgroup$
– Welsy
Jan 9 at 18:34
$begingroup$
Do you have any reference on what curve to expect from this component? Usually there should be some function with few parameters that models the behavior fairly well and have parameters you can estimate with your available data. If this is a practical problem and you do need some kind of quick interpolation, you could consider using a spline which would fit the points exactly with some smoothness properties that makes them better than linear interpolation between two points..
$endgroup$
– Mefitico
Jan 9 at 18:19
$begingroup$
Do you have any reference on what curve to expect from this component? Usually there should be some function with few parameters that models the behavior fairly well and have parameters you can estimate with your available data. If this is a practical problem and you do need some kind of quick interpolation, you could consider using a spline which would fit the points exactly with some smoothness properties that makes them better than linear interpolation between two points..
$endgroup$
– Mefitico
Jan 9 at 18:19
$begingroup$
This is an excercise for my course "Numerical methods", which requires me to use the least square methods functions provided to me. Sadly, the excercise only states: "Find a reasonable approximation of this data, using this approximation, estimate the differential entry resistance with entry voltage 0.8V and 3.5V. That's all there is.
$endgroup$
– Welsy
Jan 9 at 18:24
$begingroup$
This is an excercise for my course "Numerical methods", which requires me to use the least square methods functions provided to me. Sadly, the excercise only states: "Find a reasonable approximation of this data, using this approximation, estimate the differential entry resistance with entry voltage 0.8V and 3.5V. That's all there is.
$endgroup$
– Welsy
Jan 9 at 18:24
$begingroup$
Did you simply try polynoms ?
$endgroup$
– Damien
Jan 9 at 18:28
$begingroup$
Did you simply try polynoms ?
$endgroup$
– Damien
Jan 9 at 18:28
$begingroup$
I've tried using basic polynoms from t to t^5 but I don't really know how to choose them well enough to get somewhere. When I use polynoms from degree 1 to 8, I get accuracy alright, but it doesn't look legit, you know what I mean... i.imgur.com/oaomaga.png
$endgroup$
– Welsy
Jan 9 at 18:34
$begingroup$
I've tried using basic polynoms from t to t^5 but I don't really know how to choose them well enough to get somewhere. When I use polynoms from degree 1 to 8, I get accuracy alright, but it doesn't look legit, you know what I mean... i.imgur.com/oaomaga.png
$endgroup$
– Welsy
Jan 9 at 18:34
add a comment |
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$begingroup$
Do you have any reference on what curve to expect from this component? Usually there should be some function with few parameters that models the behavior fairly well and have parameters you can estimate with your available data. If this is a practical problem and you do need some kind of quick interpolation, you could consider using a spline which would fit the points exactly with some smoothness properties that makes them better than linear interpolation between two points..
$endgroup$
– Mefitico
Jan 9 at 18:19
$begingroup$
This is an excercise for my course "Numerical methods", which requires me to use the least square methods functions provided to me. Sadly, the excercise only states: "Find a reasonable approximation of this data, using this approximation, estimate the differential entry resistance with entry voltage 0.8V and 3.5V. That's all there is.
$endgroup$
– Welsy
Jan 9 at 18:24
$begingroup$
Did you simply try polynoms ?
$endgroup$
– Damien
Jan 9 at 18:28
$begingroup$
I've tried using basic polynoms from t to t^5 but I don't really know how to choose them well enough to get somewhere. When I use polynoms from degree 1 to 8, I get accuracy alright, but it doesn't look legit, you know what I mean... i.imgur.com/oaomaga.png
$endgroup$
– Welsy
Jan 9 at 18:34