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quadrature rule has the highest possible order
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Find the weights $w_0, w_1$ and the abscissa $x_0$ such that the following quadrature rule has the highest possible order: $$int_0^1 f(x) dx approx w_0f(x_0) + w_1 f(1)$$
Do I need to use the formula,
$$w_j = frac{2}{(1-x_j^2)
(P'_n(x_j))^2}$$
If so how do I use it? what is $x_j$ and $P'_n$?
numerical-methods
asked yesterday
user123
46319
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Find the weights $w_0, w_1$ and the abscissa $x_0$ such that the following quadrature rule has the highest possible order: $$int_0^1 f(x) dx approx w_0f(x_0) + w_1 f(1)$$
Do I need to use the formula,
$$w_j = frac{2}{(1-x_j^2)
(P'_n(x_j))^2}$$
If so how do I use it? what is $x_j$ and $P'_n$?
numerical-methods
asked yesterday
user123
46319
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Find the weights $w_0, w_1$ and the abscissa $x_0$ such that the following quadrature rule has the highest possible order: $$int_0^1 f(x) dx approx w_0f(x_0) + w_1 f(1)$$
Do I need to use the formula,
$$w_j = frac{2}{(1-x_j^2)
(P'_n(x_j))^2}$$
If so how do I use it? what is $x_j$ and $P'_n$?
numerical-methods
asked yesterday
user123
46319
Find the weights $w_0, w_1$ and the abscissa $x_0$ such that the following quadrature rule has the highest possible order: $$int_0^1 f(x) dx approx w_0f(x_0) + w_1 f(1)$$
Do I need to use the formula,
$$w_j = frac{2}{(1-x_j^2)
(P'_n(x_j))^2}$$
If so how do I use it? what is $x_j$ and $P'_n$?
numerical-methods
numerical-methods
asked yesterday
user123
46319
asked yesterday
user123
46319
asked yesterday
user123
46319
asked yesterday
user123
46319
asked yesterday
user123
46319
46319
add a comment |
add a comment |
1 Answer
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The abscissas $(x_j)$ are the zeros of the $n$th orthogonal polynomial; here $n=2$ and $P_2$ is the second Legendre polynomial (only the domain of definition has been altered from $[-1,1]$ to $[0,1]$ so you need to change variable. Read about Gaussian quadratures.
answered yesterday
Richard Martin
1,3588
I havemade another post about this question with more detail, could you help?
– user123
11 hours ago
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
The abscissas $(x_j)$ are the zeros of the $n$th orthogonal polynomial; here $n=2$ and $P_2$ is the second Legendre polynomial (only the domain of definition has been altered from $[-1,1]$ to $[0,1]$ so you need to change variable. Read about Gaussian quadratures.
answered yesterday
Richard Martin
1,3588
I havemade another post about this question with more detail, could you help?
– user123
11 hours ago
add a comment |
up vote
0
down vote
The abscissas $(x_j)$ are the zeros of the $n$th orthogonal polynomial; here $n=2$ and $P_2$ is the second Legendre polynomial (only the domain of definition has been altered from $[-1,1]$ to $[0,1]$ so you need to change variable. Read about Gaussian quadratures.
answered yesterday
Richard Martin
1,3588
I havemade another post about this question with more detail, could you help?
– user123
11 hours ago
add a comment |
up vote
0
down vote
up vote
0
down vote
The abscissas $(x_j)$ are the zeros of the $n$th orthogonal polynomial; here $n=2$ and $P_2$ is the second Legendre polynomial (only the domain of definition has been altered from $[-1,1]$ to $[0,1]$ so you need to change variable. Read about Gaussian quadratures.
answered yesterday
Richard Martin
1,3588
The abscissas $(x_j)$ are the zeros of the $n$th orthogonal polynomial; here $n=2$ and $P_2$ is the second Legendre polynomial (only the domain of definition has been altered from $[-1,1]$ to $[0,1]$ so you need to change variable. Read about Gaussian quadratures.
answered yesterday
Richard Martin
1,3588
edited yesterday
answered yesterday
Richard Martin
1,3588
answered yesterday
Richard Martin
1,3588
answered yesterday
Richard Martin
1,3588
1,3588
I havemade another post about this question with more detail, could you help?
– user123
11 hours ago
add a comment |
I havemade another post about this question with more detail, could you help?
– user123
11 hours ago
I havemade another post about this question with more detail, could you help?
– user123
11 hours ago
I havemade another post about this question with more detail, could you help?
– user123
11 hours ago
add a comment |
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