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Results tagged with numerical-integration
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user 91890
3
votes
0
answers
95
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Fast numerical integration of $\int_{[0,\:1)^d}\left|f_x(y)-g(y)\right|^p\:{\rm d}y$ for var...
Let $k\in\mathbb N$ and $y_1,\ldots,y_k\in[0,1)^d$ with $$\frac1k\sum_{i=1}^kh(y_i)\approx\int_{[0,\:1)^d}h(y)\:{\rm d}y\tag1$$ for every nice enough function $h:[0,1)^d\to\mathbb R$.
Now let $p\ge1$, …
- 167
1
vote
0
answers
218
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Numerically compute the Schwarz-Christoffel mapping to the square
I want to map the upper-half plane $$\mathbb H:=\{z\in\mathbb C:\Im(z)>0\}$$ to $[0,1)^2$ by a conformal map. If I got this right, then such a mapping is given by the Schwarz-Christoffel mapping to th …
- 167
2
votes
0
answers
76
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Minimizing $\int\lambda({\rm d}y)\frac{\left|g(y)-\frac{p(y)}c\lambda g\right|^2}{r((i,x),y)...
Let $I\subseteq\mathbb N$ be finite and nonempty, $(E,\mathcal E,\lambda)$ be a $\sigma$-finite measure space, $$\lambda f:=\int f\:{\rm d}\lambda$$ for $\lambda$-integrable $f:E\to\mathbb R$, $p:E\to …
- 167