Mixing
Lagrange Interpolation how does it work?
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I am making a program to find a polynomial given a set of data. I understand the summation of the formula. Given the image below can someone explain what the square looking symbol is next to the Li(x)? Can you explain the Li(x) function to me as well?
Lagrrange Formula
lagrange-interpolation
asked 2 days ago
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I am making a program to find a polynomial given a set of data. I understand the summation of the formula. Given the image below can someone explain what the square looking symbol is next to the Li(x)? Can you explain the Li(x) function to me as well?
Lagrrange Formula
lagrange-interpolation
asked 2 days ago
User
1
New contributor
User is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Do you mean the $Pi$ symbol? That's a product symbol.
– littleO
2 days ago
Yes, and ok can you explain how to use Li(x). I don't understand. So for every x value, we are given we calculate Li for all the x values?
– User
2 days ago
$L_i(x)$ sends $x_i$ to 1 and all other $x_j$ to 0. Thus summing up $y_i L_i(x)$ over $i$ gives an interpolant of all of the $(x_i,y_i)$.
– Ian
2 days ago
So for Li(x) we calculate the product of the formula for each j in J but we skip over the i-th element
– User
2 days ago
That is correct. This is needed so that $L_i(x_i)$ is nonzero.
– Ian
2 days ago
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I am making a program to find a polynomial given a set of data. I understand the summation of the formula. Given the image below can someone explain what the square looking symbol is next to the Li(x)? Can you explain the Li(x) function to me as well?
Lagrrange Formula
lagrange-interpolation
asked 2 days ago
User
1
New contributor
User is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
I am making a program to find a polynomial given a set of data. I understand the summation of the formula. Given the image below can someone explain what the square looking symbol is next to the Li(x)? Can you explain the Li(x) function to me as well?
Lagrrange Formula
lagrange-interpolation
lagrange-interpolation
asked 2 days ago
User
1
New contributor
User is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 days ago
User
1
New contributor
User is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 days ago
User
1
New contributor
User is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 days ago
User
1
asked 2 days ago
User
1
1
New contributor
User is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
User is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
User is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Do you mean the $Pi$ symbol? That's a product symbol.
– littleO
2 days ago
Yes, and ok can you explain how to use Li(x). I don't understand. So for every x value, we are given we calculate Li for all the x values?
– User
2 days ago
$L_i(x)$ sends $x_i$ to 1 and all other $x_j$ to 0. Thus summing up $y_i L_i(x)$ over $i$ gives an interpolant of all of the $(x_i,y_i)$.
– Ian
2 days ago
So for Li(x) we calculate the product of the formula for each j in J but we skip over the i-th element
– User
2 days ago
That is correct. This is needed so that $L_i(x_i)$ is nonzero.
– Ian
2 days ago
add a comment |
Do you mean the $Pi$ symbol? That's a product symbol.
– littleO
2 days ago
Yes, and ok can you explain how to use Li(x). I don't understand. So for every x value, we are given we calculate Li for all the x values?
– User
2 days ago
$L_i(x)$ sends $x_i$ to 1 and all other $x_j$ to 0. Thus summing up $y_i L_i(x)$ over $i$ gives an interpolant of all of the $(x_i,y_i)$.
– Ian
2 days ago
So for Li(x) we calculate the product of the formula for each j in J but we skip over the i-th element
– User
2 days ago
That is correct. This is needed so that $L_i(x_i)$ is nonzero.
– Ian
2 days ago
Do you mean the $Pi$ symbol? That's a product symbol.
– littleO
2 days ago
Do you mean the $Pi$ symbol? That's a product symbol.
– littleO
2 days ago
Yes, and ok can you explain how to use Li(x). I don't understand. So for every x value, we are given we calculate Li for all the x values?
– User
2 days ago
Yes, and ok can you explain how to use Li(x). I don't understand. So for every x value, we are given we calculate Li for all the x values?
– User
2 days ago
$L_i(x)$ sends $x_i$ to 1 and all other $x_j$ to 0. Thus summing up $y_i L_i(x)$ over $i$ gives an interpolant of all of the $(x_i,y_i)$.
– Ian
2 days ago
$L_i(x)$ sends $x_i$ to 1 and all other $x_j$ to 0. Thus summing up $y_i L_i(x)$ over $i$ gives an interpolant of all of the $(x_i,y_i)$.
– Ian
2 days ago
So for Li(x) we calculate the product of the formula for each j in J but we skip over the i-th element
– User
2 days ago
So for Li(x) we calculate the product of the formula for each j in J but we skip over the i-th element
– User
2 days ago
That is correct. This is needed so that $L_i(x_i)$ is nonzero.
– Ian
2 days ago
That is correct. This is needed so that $L_i(x_i)$ is nonzero.
– Ian
2 days ago
add a comment |
1 Answer
1
active
oldest
votes
up vote
0
down vote
Perhaps you can understand it via this example on 3 points. This Desmos graph is interactive and you can create any interpolation on 3 points with it.
answered 2 days ago
Calvin Khor
10.6k21436
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
Perhaps you can understand it via this example on 3 points. This Desmos graph is interactive and you can create any interpolation on 3 points with it.
answered 2 days ago
Calvin Khor
10.6k21436
add a comment |
up vote
0
down vote
Perhaps you can understand it via this example on 3 points. This Desmos graph is interactive and you can create any interpolation on 3 points with it.
answered 2 days ago
Calvin Khor
10.6k21436
add a comment |
up vote
0
down vote
up vote
0
down vote
Perhaps you can understand it via this example on 3 points. This Desmos graph is interactive and you can create any interpolation on 3 points with it.
answered 2 days ago
Calvin Khor
10.6k21436
Perhaps you can understand it via this example on 3 points. This Desmos graph is interactive and you can create any interpolation on 3 points with it.
answered 2 days ago
Calvin Khor
10.6k21436
answered 2 days ago
Calvin Khor
10.6k21436
answered 2 days ago
Calvin Khor
10.6k21436
answered 2 days ago
Calvin Khor
10.6k21436
10.6k21436
add a comment |
add a comment |
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Do you mean the $Pi$ symbol? That's a product symbol.
– littleO
2 days ago
Yes, and ok can you explain how to use Li(x). I don't understand. So for every x value, we are given we calculate Li for all the x values?
– User
2 days ago
$L_i(x)$ sends $x_i$ to 1 and all other $x_j$ to 0. Thus summing up $y_i L_i(x)$ over $i$ gives an interpolant of all of the $(x_i,y_i)$.
– Ian
2 days ago
So for Li(x) we calculate the product of the formula for each j in J but we skip over the i-th element
– User
2 days ago
That is correct. This is needed so that $L_i(x_i)$ is nonzero.
– Ian
2 days ago