How to program numerical integration $int_t^{infty}frac{1}{(u+1)^2}du$?
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I'm facing a problem when program the numerical integration of $int_t^{infty}frac{1}{(u+1)^2}du$, I know that the true value is $frac{1}{1+t}$, however, when I want to calculate the definite integration numerically, I found the result is very strange like following:
The blue curve is the true value, the red curve is the numerical integration.
The problem setup is that I know $X_1,X_2,cdots,X_n$ (ranges from $0$ to $1$), then I tried to program following code in matlab:
((1./(1+Xi_sort).^2).*(Xi_sort-[0;Xi_sort(1:n-1)]))'*tril(ones(n,n),0)
What's wrong with this? Thank you so much for your help.
matlab numerical-calculus
edited Dec 7 '18 at 3:08
user587192
1,841315
asked Dec 7 '18 at 1:09
caslpcaslp
42
$endgroup$
add a comment |
$begingroup$
I'm facing a problem when program the numerical integration of $int_t^{infty}frac{1}{(u+1)^2}du$, I know that the true value is $frac{1}{1+t}$, however, when I want to calculate the definite integration numerically, I found the result is very strange like following:
The blue curve is the true value, the red curve is the numerical integration.
The problem setup is that I know $X_1,X_2,cdots,X_n$ (ranges from $0$ to $1$), then I tried to program following code in matlab:
((1./(1+Xi_sort).^2).*(Xi_sort-[0;Xi_sort(1:n-1)]))'*tril(ones(n,n),0)
What's wrong with this? Thank you so much for your help.
matlab numerical-calculus
edited Dec 7 '18 at 3:08
user587192
1,841315
asked Dec 7 '18 at 1:09
caslpcaslp
42
$endgroup$
$begingroup$
Could you post all the code you use instead of just a piece of it?
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– user587192
Dec 7 '18 at 2:57
1
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The red one is the integral from $t$ to $1$, not $infty$
$endgroup$
– Empy2
Dec 7 '18 at 3:35
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@Empy2 I see, thank you. But I cannot change the range of $X_1$ to $X_2$, how can I remedy this in code? Will interpolation work?
$endgroup$
– caslp
Dec 7 '18 at 4:02
add a comment |
$begingroup$
I'm facing a problem when program the numerical integration of $int_t^{infty}frac{1}{(u+1)^2}du$, I know that the true value is $frac{1}{1+t}$, however, when I want to calculate the definite integration numerically, I found the result is very strange like following:
The blue curve is the true value, the red curve is the numerical integration.
The problem setup is that I know $X_1,X_2,cdots,X_n$ (ranges from $0$ to $1$), then I tried to program following code in matlab:
((1./(1+Xi_sort).^2).*(Xi_sort-[0;Xi_sort(1:n-1)]))'*tril(ones(n,n),0)
What's wrong with this? Thank you so much for your help.
matlab numerical-calculus
edited Dec 7 '18 at 3:08
user587192
1,841315
asked Dec 7 '18 at 1:09
caslpcaslp
42
$endgroup$
I'm facing a problem when program the numerical integration of $int_t^{infty}frac{1}{(u+1)^2}du$, I know that the true value is $frac{1}{1+t}$, however, when I want to calculate the definite integration numerically, I found the result is very strange like following:
The blue curve is the true value, the red curve is the numerical integration.
The problem setup is that I know $X_1,X_2,cdots,X_n$ (ranges from $0$ to $1$), then I tried to program following code in matlab:
((1./(1+Xi_sort).^2).*(Xi_sort-[0;Xi_sort(1:n-1)]))'*tril(ones(n,n),0)
What's wrong with this? Thank you so much for your help.
matlab numerical-calculus
matlab numerical-calculus
edited Dec 7 '18 at 3:08
user587192
1,841315
asked Dec 7 '18 at 1:09
caslpcaslp
42
edited Dec 7 '18 at 3:08
user587192
1,841315
asked Dec 7 '18 at 1:09
caslpcaslp
42
edited Dec 7 '18 at 3:08
user587192
1,841315
edited Dec 7 '18 at 3:08
user587192
1,841315
edited Dec 7 '18 at 3:08
user587192
1,841315
1,841315
asked Dec 7 '18 at 1:09
caslpcaslp
42
asked Dec 7 '18 at 1:09
caslpcaslp
42
asked Dec 7 '18 at 1:09
caslpcaslp
42
42
$begingroup$
Could you post all the code you use instead of just a piece of it?
$endgroup$
– user587192
Dec 7 '18 at 2:57
1
$begingroup$
The red one is the integral from $t$ to $1$, not $infty$
$endgroup$
– Empy2
Dec 7 '18 at 3:35
$begingroup$
@Empy2 I see, thank you. But I cannot change the range of $X_1$ to $X_2$, how can I remedy this in code? Will interpolation work?
$endgroup$
– caslp
Dec 7 '18 at 4:02
add a comment |
$begingroup$
Could you post all the code you use instead of just a piece of it?
$endgroup$
– user587192
Dec 7 '18 at 2:57
1
$begingroup$
The red one is the integral from $t$ to $1$, not $infty$
$endgroup$
– Empy2
Dec 7 '18 at 3:35
$begingroup$
@Empy2 I see, thank you. But I cannot change the range of $X_1$ to $X_2$, how can I remedy this in code? Will interpolation work?
$endgroup$
– caslp
Dec 7 '18 at 4:02
$begingroup$
Could you post all the code you use instead of just a piece of it?
$endgroup$
– user587192
Dec 7 '18 at 2:57
$begingroup$
Could you post all the code you use instead of just a piece of it?
$endgroup$
– user587192
Dec 7 '18 at 2:57
1
1
$begingroup$
The red one is the integral from $t$ to $1$, not $infty$
$endgroup$
– Empy2
Dec 7 '18 at 3:35
$begingroup$
The red one is the integral from $t$ to $1$, not $infty$
$endgroup$
– Empy2
Dec 7 '18 at 3:35
$begingroup$
@Empy2 I see, thank you. But I cannot change the range of $X_1$ to $X_2$, how can I remedy this in code? Will interpolation work?
$endgroup$
– caslp
Dec 7 '18 at 4:02
$begingroup$
@Empy2 I see, thank you. But I cannot change the range of $X_1$ to $X_2$, how can I remedy this in code? Will interpolation work?
$endgroup$
– caslp
Dec 7 '18 at 4:02
add a comment |
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$begingroup$
Could you post all the code you use instead of just a piece of it?
$endgroup$
– user587192
Dec 7 '18 at 2:57
1
$begingroup$
The red one is the integral from $t$ to $1$, not $infty$
$endgroup$
– Empy2
Dec 7 '18 at 3:35
$begingroup$
@Empy2 I see, thank you. But I cannot change the range of $X_1$ to $X_2$, how can I remedy this in code? Will interpolation work?
$endgroup$
– caslp
Dec 7 '18 at 4:02