diff options
Diffstat (limited to 'anm/n4.lyx')
| -rw-r--r-- | anm/n4.lyx | 46 |
1 files changed, 24 insertions, 22 deletions
@@ -181,15 +181,15 @@ Sean \end_inset las sucesiones dadas por -\begin_inset Formula $x_{0}:=p$ +\begin_inset Formula $x_{0}\coloneqq p$ \end_inset , -\begin_inset Formula $x_{k+1}:=Ax_{k}$ +\begin_inset Formula $x_{k+1}\coloneqq Ax_{k}$ \end_inset y -\begin_inset Formula $r_{k}:=\frac{\langle x_{k+1},y\rangle}{\langle x_{k},y\rangle}$ +\begin_inset Formula $r_{k}\coloneqq \frac{\langle x_{k+1},y\rangle}{\langle x_{k},y\rangle}$ \end_inset , entonces @@ -214,7 +214,7 @@ Sean Demostración: \series default Sean -\begin_inset Formula $\phi(x):=\langle x,y\rangle$ +\begin_inset Formula $\phi(x)\coloneqq \langle x,y\rangle$ \end_inset , @@ -317,11 +317,11 @@ En la práctica no se calcula \end_inset dada por -\begin_inset Formula $y_{0}:=\frac{x_{0}}{\Vert x_{0}\Vert}$ +\begin_inset Formula $y_{0}\coloneqq \frac{x_{0}}{\Vert x_{0}\Vert}$ \end_inset e -\begin_inset Formula $y_{k+1}:=\frac{Ay_{k}}{\Vert Ay_{k}\Vert}$ +\begin_inset Formula $y_{k+1}\coloneqq \frac{Ay_{k}}{\Vert Ay_{k}\Vert}$ \end_inset , y entonces @@ -457,7 +457,7 @@ método de Jacobi de giros en planos determinados por dos vectores de la base canónica de forma que -\begin_inset Formula $(A_{k}:=(O_{1}\cdots O_{k})^{t}A(O_{1}\cdots O_{k}))_{k}$ +\begin_inset Formula $(A_{k}\coloneqq (O_{1}\cdots O_{k})^{t}A(O_{1}\cdots O_{k}))_{k}$ \end_inset , que podemos obtener como @@ -481,7 +481,7 @@ Sean \end_inset , -\begin_inset Formula $A:=(a_{ij})\in{\cal M}_{n}(\mathbb{R})$ +\begin_inset Formula $A\coloneqq (a_{ij})\in{\cal M}_{n}(\mathbb{R})$ \end_inset simétrica, @@ -689,7 +689,7 @@ egroup \end_inset y -\begin_inset Formula $B:=(b_{ij}):=O^{t}AO$ +\begin_inset Formula $B\coloneqq (b_{ij})\coloneqq O^{t}AO$ \end_inset , entonces: @@ -839,7 +839,7 @@ de donde se obtiene la primera parte del enunciado. \end_inset , y dada -\begin_inset Formula $C:=(c_{ij})\in{\cal M}_{n}(\mathbb{R})$ +\begin_inset Formula $C\coloneqq (c_{ij})\in{\cal M}_{n}(\mathbb{R})$ \end_inset , @@ -885,7 +885,7 @@ Para el \end_inset descrito en el apartado anterior, sean -\begin_inset Formula $x:=\frac{a_{qq}-a_{pp}}{2a_{pq}}$ +\begin_inset Formula $x\coloneqq \frac{a_{qq}-a_{pp}}{2a_{pq}}$ \end_inset , @@ -900,11 +900,11 @@ t:=\begin{cases} \end_inset -\begin_inset Formula $c:=\frac{1}{\sqrt{1+t^{2}}}$ +\begin_inset Formula $c\coloneqq \frac{1}{\sqrt{1+t^{2}}}$ \end_inset y -\begin_inset Formula $s:=\frac{t}{\sqrt{1+t^{2}}}$ +\begin_inset Formula $s\coloneqq \frac{t}{\sqrt{1+t^{2}}}$ \end_inset , para @@ -926,11 +926,11 @@ b_{pi}=b_{ip} & =ca_{ip}-sa_{iq}, & b_{qi}=b_{iq} & =sa_{ip}+ca_{iq}, & b_{ij} & \begin_deeper \begin_layout Standard Sean -\begin_inset Formula $x:=\frac{a_{qq}-a_{pp}}{2a_{pq}}$ +\begin_inset Formula $x\coloneqq \frac{a_{qq}-a_{pp}}{2a_{pq}}$ \end_inset y -\begin_inset Formula $t:=\tan\theta$ +\begin_inset Formula $t\coloneqq \tan\theta$ \end_inset . @@ -1036,7 +1036,9 @@ status open \backslash -Entrada{Matriz simétrica real $A:=(a_{ij})$ de tamaño $n$ y nivel de tolerancia +Entrada{Matriz simétrica real $A +\backslash +coloneqq (a_{ij})$ de tamaño $n$ y nivel de tolerancia a errores $e>0$.} \end_layout @@ -1644,7 +1646,7 @@ Para la primera parte del teorema, sean \end_inset y -\begin_inset Formula $\varepsilon_{k}:=\sum_{i\neq j}(a_{kij})^{2}$ +\begin_inset Formula $\varepsilon_{k}\coloneqq \sum_{i\neq j}(a_{kij})^{2}$ \end_inset . @@ -1747,7 +1749,7 @@ de donde \begin_layout Standard Sea -\begin_inset Formula $D_{k}:=\text{diag}(a_{k11},\dots,a_{knn})$ +\begin_inset Formula $D_{k}\coloneqq \text{diag}(a_{k11},\dots,a_{knn})$ \end_inset . @@ -2096,11 +2098,11 @@ Dada una matriz \end_inset como -\begin_inset Formula $A_{0}:=A$ +\begin_inset Formula $A_{0}\coloneqq A$ \end_inset y -\begin_inset Formula $A_{k+1}:=R_{k}Q_{k}$ +\begin_inset Formula $A_{k+1}\coloneqq R_{k}Q_{k}$ \end_inset , donde @@ -2119,11 +2121,11 @@ Dada una matriz \begin_layout Standard Para obtener una aproximación de los valores propios a partir de una aproximació n -\begin_inset Formula $A_{p}:=(u_{ij})$ +\begin_inset Formula $A_{p}\coloneqq (u_{ij})$ \end_inset de dicha matriz, definimos una matriz -\begin_inset Formula $V:=(v_{ij})\in{\cal M}_{n}$ +\begin_inset Formula $V\coloneqq (v_{ij})\in{\cal M}_{n}$ \end_inset dada por |