diff options
Diffstat (limited to 'anm/n5.lyx')
| -rw-r--r-- | anm/n5.lyx | 20 |
1 files changed, 10 insertions, 10 deletions
@@ -319,7 +319,7 @@ Sean \end_inset y -\begin_inset Formula $x_{k+1}:=f(x_{k})$ +\begin_inset Formula $x_{k+1}\coloneqq f(x_{k})$ \end_inset converge. @@ -343,7 +343,7 @@ begin{samepage} \begin_layout Standard Sean -\begin_inset Formula $R:=[a_{1},b_{1}]\times\dots\times[a_{n},b_{n}]$ +\begin_inset Formula $R\coloneqq [a_{1},b_{1}]\times\dots\times[a_{n},b_{n}]$ \end_inset , @@ -399,7 +399,7 @@ La aceleración de Gauss-Seidel \series default de una iteración de punto fijo consiste en considerar, en vez de -\begin_inset Formula $x_{k+1}:=g(x_{k})$ +\begin_inset Formula $x_{k+1}\coloneqq g(x_{k})$ \end_inset , @@ -483,11 +483,11 @@ teorema \end_inset , la sucesión dada por -\begin_inset Formula $x_{0}:=x$ +\begin_inset Formula $x_{0}\coloneqq x$ \end_inset y -\begin_inset Formula $x_{k+1}:=x_{k}-df(x_{k})^{-1}f(x_{k})$ +\begin_inset Formula $x_{k+1}\coloneqq x_{k}-df(x_{k})^{-1}f(x_{k})$ \end_inset converge a @@ -523,7 +523,7 @@ Demostración : \series default Queremos ver que -\begin_inset Formula $g(x):=x-df(x)^{-1}f(x)$ +\begin_inset Formula $g(x)\coloneqq x-df(x)^{-1}f(x)$ \end_inset es contractiva cerca de @@ -660,7 +660,7 @@ Para \end_inset dada por -\begin_inset Formula $\varphi(t):=f(y+t(x-y))$ +\begin_inset Formula $\varphi(t)\coloneqq f(y+t(x-y))$ \end_inset , por la regla de la cadena, @@ -703,7 +703,7 @@ Cuando esto se cumple, \end_inset y tomando -\begin_inset Formula $M:=\frac{K}{2}\sup_{x\in B(\xi,r)}\Vert df(x)^{-1}\Vert$ +\begin_inset Formula $M\coloneqq \frac{K}{2}\sup_{x\in B(\xi,r)}\Vert df(x)^{-1}\Vert$ \end_inset se obtiene la acotación. @@ -759,7 +759,7 @@ A_{k}:=A_{k-1}+\frac{1}{\Vert x_{k}-x_{k-1}\Vert_{2}^{2}}f(x_{k})(x_{k}-x_{k-1}) \end_inset tomando -\begin_inset Formula $A_{0}:=df(x_{0})$ +\begin_inset Formula $A_{0}\coloneqq df(x_{0})$ \end_inset . @@ -1137,7 +1137,7 @@ noprefix "false" \end_inset , y consiste en minimizar la función -\begin_inset Formula $g(x):=\Vert f(x)\Vert_{2}^{2}$ +\begin_inset Formula $g(x)\coloneqq \Vert f(x)\Vert_{2}^{2}$ \end_inset desplazándonos, en cada iteración, en la dirección de mayor descenso en |