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frechet_derivative [2014/01/31 16:46] nikolaj |
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===== Fréchet derivative ===== | ===== Fréchet derivative ===== | ||
==== Set ==== | ==== Set ==== | ||
- | | @#88DDEE: $X,Y$ ... Banach spaces with topology | | + | | @#55CCEE: context | @#55CCEE: $X,Y$ ... Banach spaces with topology | |
- | | @#88DDEE: $\mathcal O$ ... open in $X$ | | + | | @#55CCEE: context | @#55CCEE: $\mathcal O$ ... open in $X$ | |
- | | @#FFBB00: $D:\mathrm{Continuous}(\mathcal O,Y)\to \mathrm{Continuous}(\mathcal O,\mathrm{BoundedLinOp}(X,Y))$ | | + | | @#FFBB00: definiendum | @#FFBB00: $D:\mathrm{Continuous}(\mathcal O,Y)\to \mathrm{Continuous}(\mathcal O,\mathrm{BoundedLinOp}(X,Y))$ | |
- | | @#FFBB00: $Df:=x\mapsto J_x^f$ | | + | | @#FFBB00: definiendum | @#FFBB00: $Df:=x\mapsto J_x^f$ | |
For $J_x f$, see [[Linear approximation]]. | For $J_x f$, see [[Linear approximation]]. | ||
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Wikipedia: [[http://en.wikipedia.org/wiki/Derivative_of_a_function|Derivative of a function]], [[http://en.wikipedia.org/wiki/Fr%C3%A9chet_derivative|Fréchet derivative]] | Wikipedia: [[http://en.wikipedia.org/wiki/Derivative_of_a_function|Derivative of a function]], [[http://en.wikipedia.org/wiki/Fr%C3%A9chet_derivative|Fréchet derivative]] | ||
==== Parents ==== | ==== Parents ==== | ||
- | === Requirements === | + | === Context === |
[[Linear approximation]] | [[Linear approximation]] |