/[escript]/release/3.4.2/doc/inversion/Regularization.tex
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revision 4122 by gross, Thu Dec 20 05:42:35 2012 UTC revision 4142 by gross, Tue Jan 15 09:06:06 2013 UTC
# Line 146  and for $X$ Line 146  and for $X$
146  \\  \\
147  \end{array}  \end{array}
148  \end{equation}    \end{equation}  
149  We also need to provide an approximation of the inverse of the Hessian operator. The operator evaluation is executes as a solution  We also need to provide an approximation of the inverse of the Hessian operator as discussed in section~\ref{chapter:ref:inversion cost function:gradient}.
 of a linear PDE which is solved using \escript \class{LinearPDE} class. In the \escript notation we need to provide  
 \begin{equation}\label{ref:EQU:REG:600}  
 \begin{array}{rcl}  
  A_{kilj} & = & \displaystyle{\frac{\partial X_{ki}}{\partial m_{l,j}}} \\  
 D_{kl} & =  &  \displaystyle{\frac{\partial Y_{k}}{\partial m_{l}}}  
 \end{array}  
 \end{equation}  
150  For the case of a single valued level set function $m$ we get  For the case of a single valued level set function $m$ we get
151  \begin{equation}\label{ref:EQU:REG:601}  \begin{equation}\label{ref:EQU:REG:601}
152  \begin{array}{rcl}  \begin{array}{rcl}

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