# Subversion Repositoriesslepc-dev

## Ignore whitespace Rev 2091 → Rev 2092

/trunk/docs/manual/st.tex
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 \end{Verbatim} where \texttt{type} can be one of \texttt{STSHIFT}, \texttt{STFOLD}, \texttt{STSINV}, \texttt{STCAYLEY} or \texttt{STSHELL}. \texttt{STSINVERT}, \texttt{STCAYLEY}, or \texttt{STSHELL}. The \ident{ST} type can also be set with the command-line option \Verb!-st_type! followed by the name of the method (see Table \ref{tab:transforms}). The first four spectral transformations are described in detail in the rest of this section. The last possibility, \texttt{STSHELL}, uses a specific, application-provided spectral transformation. Section \ref{sec:shell} describes how to implement one of these transformations. \begin{table}
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 Spectral Transformation & \ident{STType} & {\footnotesize Name} & Operator\\\hline Shift of Origin & \texttt{STSHIFT} & \texttt{shift} & $B^{-1}A+\sigma I$\\ Spectrum Folding & \texttt{STFOLD} & \texttt{fold} & $(B^{-1}A-\sigma I)^2$\\ Shift-and-invert & \texttt{STSINV} & \texttt{sinvert} & $(A-\sigma B)^{-1}B$\\ Cayley & \texttt{STCAYLEY} & \texttt{cayley} & $(A-\sigma B)^{-1}(A+\nu B)$\\ Shift-and-invert & \texttt{STSINVERT}& \texttt{sinvert} & $(A-\sigma B)^{-1}B$\\ Generalized Cayley & \texttt{STCAYLEY} & \texttt{cayley} & $(A-\sigma B)^{-1}(A+\nu B)$\\ Shell Transformation & \texttt{STSHELL} & \texttt{shell} & \emph{user-defined}\\\hline \end{tabular} } \caption{\label{tab:transforms}Spectral transformations available in the \ident{ST} package.}
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 \subsection{Shift-and-invert} The shift-and-invert spectral transformation (\texttt{STSINV}) is used to enhance convergence of eigenvalues in the neighborhood of a given value. In this case, the solver deals with the expressions The shift-and-invert spectral transformation (\texttt{STSINVERT}) is used to enhance convergence of eigenvalues in the neighborhood of a given value. In this case, the solver deals with the expressions \begin{eqnarray} (A-\sigma I)^{-1}x=\theta x\;\;,\\ (A-\sigma B)^{-1}B x=\theta x\;\;,