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committedFeb 21, 2019
Fixed a few references
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‎linear_operators_overview.tex

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%!TeX shellEscape = restricted
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% !TEX program = pdflatex
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%!TeX enableSynctex = true
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\documentclass[11pt]{article}
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\usepackage{url,amsmath,amsfonts}
@@ -285,7 +286,7 @@ \subsection{Stationary HJBE with Reflecting Barriers}\label{sec:simple-reflectin
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\end{align}
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Since $Q_b = 0$ in this case, interiors are solved as
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\begin{align}
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u = (L Q_L)^{-1}x
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u = (L Q_L)^{-1}x\label{solve_u_hat_in_terms_of_interiors}
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\end{align}
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%Then, by \cref{solve_u_hat_cond_2}, we can solve the extended state vector by
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% \begin{align}
@@ -368,7 +369,7 @@ \subsection{Stationary HJBE with Only Drift}
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\end{align}
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We first consider a one-dimension case where $x\in [x^{\min},x^{\max}]$. Let $M_E = 2$ and thereby $\Delta = \frac{x^{\max}-x^{\min}}{\bar{M}}$ and $\bar{M} = M+2$.
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Considering $\mu>0$, we must choose the forward first difference, thus the matrix form of operator $\tilde{L}$ can be defined as $L = \mu L_1^+$ as in \cref{eq:L-1p}. Analogously, for $\mu<0$, we must choose the backward first difference, which implies that the matrix form of operator $\tilde{L}$ can be defined as $L = \mu L_1^-$ as in \cref{eq:L-1m}.
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Considering $\mu>0$, we must choose the forward first difference, thus the matrix form of operator $\tilde{L}$ can be defined as $L = \mu L_1^+$. Analogously, for $\mu<0$, we must choose the backward first difference, which implies that the matrix form of operator $\tilde{L}$ can be defined as $L = \mu L_1^-$% as in \cref{eq:L-1m}.
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Considering the absorbing barriers, we can define $B$ just like as $B_{AA}$ in \cref{eq:B-AA} and then we have
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\begin{equation}

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