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stevengj committed Jul 25, 2023
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4 changes: 2 additions & 2 deletions docs/src/gauss-kronrod.md
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Expand Up @@ -91,7 +91,7 @@ fewer points $n' < n$, and use their *difference* as an error
estimate. (If the error is rapidly converging with $n$, this is usually
a conservative upper bound on the error.)
```math
\mbox{error estimate} \lesssim \left|
\mbox{error estimate} = \left|
\underbrace{\sum_{i=1}^n w_i f(x_i)}_\mbox{first rule} -
\underbrace{\sum_{j=1}^{n'} w_j' f(x_j')}_\mbox{second rule}
\right|
Expand Down Expand Up @@ -198,7 +198,7 @@ julia> [x[2:2:end] gw] # embedded Gauss points ≤ 0 and weights
-0.90618 0.236927
-0.538469 0.478629
0.0 0.568889
```
```
Of course, you still have to evaluate $f(x)$ at all $2n+1$ points,
but summing the results requires a bit less arithmetic
and storing the rule takes less memory. Note also that the $(-1,1)$ rule can be applied to any desired interval $(a,b)$ by a change of variables
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