⟦1316cd710⟧

TextFile


% /u/lex2/agw/ibc/ibc.sty, Thu Jul  9 10:02:23 1987, edit by agw

\documentstyle{amsppt}

\font\twelverm=cmr12
\font\twelvebf=cmbx12

\def\makeatletter{\catcode`\@=11\relax}
\def\makeatother{\catcode`\@=12\relax}
\makeatletter

\def\B@{B } \def\D@{D }
\def\askstyle{\immediate\write\sixt@@n{Do you want B(ook style)
 or D(raft style)?  (Type B or D, follow by <return>:) }\loop
 \read\m@ne to\ans@
 \xdef\next{\def\noexpand\Ans@{\ans@}}%
 \uppercase\expandafter{\next}%
 \ifx\Ans@\B@\badans@false\bookstyle\else
 \ifx\Ans@\D@\badans@false\draftstyle\else
 \badans@true\fi\fi
 \ifbadans@\immediate\write\sixt@@n{Type B or D, follow by <return>: }%
 \repeat}

\def\bookstyle{\hsize=28truepc\vsize=46truepc}
\def\draftstyle{\magnification 1200\parindent=10pt\baselineskip=15pt}
\askstyle

\newif\iftitle			% for title pages of chapters
\titlefalse			% in case we start in the middle of a chapter

\def\chapterbeg#1#2{
   \global\titletrue
   \vfill\eject
   \null\vskip 8 truepc
   \centerline{\twelverm Chapter #1}
   \line{\hrulefill}
   \centerline{\twelvebf #2}
   \global\def\chaptertitle{#1. \lowercase{#2}}
   \global\def\currentsectiontitle{\lowercase{#2}}
   \message{#1. #2: }
   \null\vskip 9 truepc
}

\def\unnumberedchapterbeg#1{
   \global\titletrue
   \null\vskip 8 truepc
   \vskip 12 pt
   \line{\hrulefill}
   \centerline{\twelvebf #1}
   \global\def\chaptertitle{\lowercase{#1}}
   \global\def\currentsectiontitle{\lowercase{#1}}
   \message{#1}
   \null\vskip 9 truepc
}

\def\sectionbeg#1#2\medskip{
   \vskip 2 truepc
   \centerline{\bf #1.  #2}
   \nopagebreak\vskip 1truepc\nopagebreak
   \global\def\currentsectiontitle{#1. \lowercase{#2}}
   \message{#1. #2}
}

\newif\if@nobreak \@nobreakfalse 
\newif\ifignore
\def\@makeother#1{\catcode`#112\relax}
\def\newwrite{\alloc@7\write\chardef\sixt@@n}
\newwrite\@unused
\def\typeout#1{{\let\protect\string\immediate\write\@unused{#1}}}

\newdimen\@savsk
\newcount\@savsf

\def\@bsphack{\@savsk\lastskip 
    \ifhmode\@savsf\spacefactor\fi}

\def\@esphack{\relax\ifhmode\spacefactor\@savsf
     {}\ifdim \@savsk >\z@ \global\ignoretrue \ignorespaces 
  \fi \fi}

\def\@sanitize{\@makeother\ \@makeother\\\@makeother\$\@makeother\&%
\@makeother\#\@makeother\^\@makeother\^^K\@makeother\_\@makeother\^^A%
\@makeother\%\@makeother\~}

\def\makeindex{\newwrite\@indexfile
  \immediate\openout\@indexfile=\jobname.idx
  \def\index{\@bsphack\begingroup\@sanitize\@wrindex\@indexfile}
  \typeout{Writing index file \jobname.idx }}

\def\thepage{\the\pageno}

\def\@wrindex#1#2{\let\thepage\relax
   \xdef\gtempa{\write#1{\string
      \indexentry{#2}{\thepage}}}\endgroup\gtempa
   \if@nobreak \ifvmode\@nobreak\fi\fi\@esphack}

\def\index{\@bsphack\begingroup\@sanitize\@index}
\def\@index#1{\endgroup\@esphack}

\def\@idxitem{\par\hangindent 40pt}
\def\subitem{\par\hangindent 40pt \hskip 20pt}
\def\subsubitem{\par\hangindent 40pt \hskip 30pt}
\def\indexspace{\par \vskip 10pt plus 5pt minus 3pt\relax}

\def\beginindex{\begingroup\let\item\@idxitem\begindoublecolumns}
\def\endindex{\enddoublecolumns\endgroup}

\newbox\partialpage
\newdimen\pagewidth  \pagewidth=\hsize
\newdimen\pageheight \pageheight=\vsize
\newdimen\colwidth \colwidth=\pagewidth  \divide\colwidth by 2
\newdimen\twicecolheight \twicecolheight=\pageheight 
   \multiply\twicecolheight by 2
   \advance\twicecolheight by 1truepc  % well, a little more than twice
\def\begindoublecolumns{\begingroup
  \output={\global\setbox\partialpage=\vbox{\unvbox255\bigskip}}\eject
  \raggedright
  \output={\splitcolumns} 
  \hsize=\colwidth
  \vsize=\twicecolheight
  \let\item\@idxitem}
\def\enddoublecolumns{\output={\balancecolumns}\eject
  \endgroup \pagegoal=\vsize}
\def\splitcolumns{\splittopskip=\topskip \splitmaxdepth=\maxdepth
  \dimen@=\pageheight \advance\dimen@ by-\ht\partialpage
  \setbox0=\vsplit255 to\dimen@ \setbox2=\vsplit255 to\dimen@
  \unvbox255 \penalty\outputpenalty
  \doublecolumnout}
\def\doublecolumnout{\shipout\vbox{%
       \hsize=\pagewidth
       \iftitle\else\makeheadline\fi%
       \unvbox\partialpage
       \wd0=\colwidth \wd2=\colwidth
       \hbox to\pagewidth{\box0\hfil\box2}
       \iftitle\makefootline\global\titlefalse\fi
       \hsize=\colwidth}
  \advancepageno
  \global\def\sectiontitle{\currentsectiontitle}
  \ifnum\outputpenalty>-\@MM \else\dosupereject\fi}

\def\balancecolumns{\setbox0=\vbox{\unvbox255} \dimen@=\ht0
  \advance\dimen@ by\topskip \advance\dimen@ by-\baselineskip
  \divide\dimen@ by2 \splittopskip=\topskip
  {\vbadness=10000 \loop \global\setbox3=\copy0
    \global\setbox1=\vsplit3 to\dimen@
    \ifdim\ht3>\dimen@ \global\advance\dimen@ by1pt \repeat}
  \setbox0=\vbox to\dimen@{\unvbox1}
  \setbox2=\vbox to\dimen@{\unvbox3}
  \doublecolumnout}

\output={\ibcoutput}

\def\leftheadline{\eightbf\folio\hfil\smc\chaptertitle}
\def\rightheadline{\smc\sectiontitle\hfil\eightbf\folio}
\headline={\ifodd\pageno\rightheadline\else\leftheadline\fi}

\def\leftfootline{\eightbf\folio\hfil}
\def\rightfootline{\eightbf\hfil\folio}
\footline={\ifodd\pageno\rightfootline\else\leftfootline\fi}

\def\ibcoutput{\shipout\vbox{%
       \iftitle\else\makeheadline\fi
       \pagebody
       \iftitle\makefootline\global\titlefalse\fi}
  \advancepageno
  \global\def\sectiontitle{\currentsectiontitle}
  \ifnum\outputpenalty>-\@MM \else\dosupereject\fi}

\def\Y@{Y } \def\N@{N }
\def\makingindex{\immediate\write\sixt@@n{Do you want to make an 
index?  (Type Y or N, follow by <return>:) }\loop
 \read\m@ne to\ans@
 \xdef\next{\def\noexpand\Ans@{\ans@}}%
 \uppercase\expandafter{\next}%
 \ifx\Ans@\Y@\badans@false\makeindex\else
 \ifx\Ans@\N@\badans@false\else
 \badans@true\fi\fi
 \ifbadans@\immediate\write\sixt@@n{Type Y or N, follow by <return>: }%
 \repeat}
\makingindex

\makeatother

% various abbreviations ... form Greg and Henryk

\define\a{\operatorname{a}}
\define\avg{\operatorname{avg}}
\define\card{\operatorname{card}}
\define\codim{\operatorname{codim}}
\define\comp{\operatorname{comp}}
\define\cost{\operatorname{cost}}
\define\trace{\operatorname{trace}}
\define\diam{\operatorname{diam}}
\define\dist{\operatorname{dist}}
\define\e{\varepsilon}
\define\E{\operatorname{E}}
\define\error{\operatorname{error}}
\define\non{\operatorname{non}}
\define\nor{\operatorname{nor}}
\define\sspan{\operatorname{span}}
\define\var{\operatorname{var}}
\define\ER{\operatorname{ER}}
\define\HH{\operatorname{H}}
\define\ter{\operatorname{ter}}
\define\pre{\operatorname{pre}}
\define\prob{\operatorname{prob}}
\define\prerel{\operatorname{pre-rel}}
\define\rad{\operatorname{rad}}
\define\ran{\operatorname{ran}}
\define\wor{\operatorname{wor}}
\define\rel{\operatorname{rel}}
\define\REL{\operatorname{REL}}
\define\per{\operatorname{per}}
\define\sign{\operatorname{sign}}
\define\infp{\operatornamewithlimits{inf\vphantom{p}}} 
\define\maxp{\operatornamewithlimits{max\vphantom{p}}} 
\define\Prob{\operatorname{Prob}} 
\def\reals{\operatorname{I\negthinspace\bold R}}
\def\Re{\reals}
\def\complexes{\operatorname{\bold C}}
\define\ofi{\overline \phi }
\define\ofig{\overline {\phi^*}}
\define\ofis{\overline {\phi^s}}
\define\on{\overline N }
\define\norm{||Sf-\phi_n(N_n(f))||}
\define\norg{||Sf-\phi_n^*\,(N_n(f))||}
\define\nors{||Sf-\phi_n^s\,(N_n(f))||}
\define\ong{\overline {N^*}}
\define\ongg{\overline {N^{**}}}
\define\nnn{N^{\non}}
\define\kr{\operatorname{kr}}
\define\mr{\operatorname{mr}}
\define\gmr{\operatorname{gmr}}
\def\bullet{\raise.5ex\hbox{\bf .}}
\def\liminf{\mathop{\underline{\text{lim}}}}

% various abbreviations ... from Art

\def\epsilon{\varepsilon}
\def\COMP{\operatorname{\hbox{\smc comp}}}
\def\esssup{\operatornamewithlimits{ess\ sup}}
\def\FEM{\operatorname{\hbox{\smc fem}}}
\def\FEMQ{\operatorname{\hbox{\smc femq}}}
\def\interior{\operatorname{int}}
\def\lin{\operatorname{lin}}
\def\range{\operatorname{ran}}
\def\SPLINE{\operatorname{\hbox{\smc spline}}}
\def\ter{\operatorname{ter}}
\def\volume{\operatorname{vol}}
\define\Lstd{\Lambda^{\operatorname{std}}}
\define\MFEM{\operatorname{\hbox{\smc mfem}}}

%\def\reals{\Bbb R}
%\def\complexes{\Bbb C}
\def\reals{\operatorname{I\negthinspace\bold R}}

%---For remarks and the like
\define\demonp#1{\demo\nofrills{#1\usualspace}}

%---Start a new section
\define\subsection#1{\par\vskip 1pc\noindent{\bf #1} 
   \nopagebreak\medskip\nopagebreak}

%---Start and end the Notes & Remarks/Exercises (smaller type, single space)
\define\startNRE{\bgroup\eightpoint\parindent=5pt}
\define\endNRE{\egroup}
\define\NR #1 {\noindent{\bf NR #1: }}	% Notes and Remarks
\define\Ex #1 {\noindent{\bf E #1: }}	% Exercises

% angle brackets for inner products
\define\<{\langle}
\define\>{\rangle}

% Script letters and other useful control sequences
\define\Sscr{{\Cal S}}
\define\Tscr{{\Cal T}}
\define\Sn{{\Cal S}_{n,k}}
\define\Tn{{\Cal T}_n}
\define\Snset{\{\Sn\}_{n=1}^\infty}
\define\Tnset{\{\Tn\}_{n=1}^\infty}

\define\phisn{\phi^{\operatorname{s}}_{n,k}}

% Needed for References

\define\BabAz{Babu\u ska and Aziz~[72]}
\define\Bakhvalov{Bakhvalov~[77]}
\define\Carasso{Carasso and Stone~[75]}
\define\Ciarlet{Ciarlet~[78]}
\define\CiarletRaviart{Ciarlet and Raviart~[72]}
\define\Dunford{Dunford and Schwartz~[63]}
\define\Dunn{Dunn~[67]}
\define\Emel{Emelyanov and Ilin~[67]}
\define\Fried{Fried~[73]}
\define\Gehatia{Gehatia and Wiff~[70]}
\define\Gelfand{Gel'fand and Vilenkin~[64]}
\define\Hadamard{Hadamard~[52]}
\define\Hammerlin{H\"ammerlin and Hoffman~[83]}
\define\Kuo{Kuo~[75]}
\define\Lattes{Lattes and Lions~[69]}
\define\Morozov{Morozov~[85]}
\define\OdRed{Oden and Reddy~[76]}
\define\Pinkus{Pinkus~[85]}
\define\Poggio{Poggio, Torre, and Koch~[85]}
\define\Pour{Pour-El and Richards~[83]}
\define\Rokhlin{Rokhlin~[86]}
\define\Shilov{Shilov and Fan Dyk Tin~[67]}
\define\Skorohod{Skorohod~[74]}
\define\Tikhonov{Tikhonov~[63]}
\define\TikhonovArsenin{Tikhonov and Arsenin~[77]}
\define\GTOA{GOTA}
\define\Twomey{Twomey~[77]}
\define\GregVarying{Wasilkowski~[86]}			%needed?
\define\WWAvg{Wasilkowski and Wo\'zniakowski~[84]}	%needed?
\define\SecondOrder{Werschulz~[82]}
\define\Fredholm{Werschulz~[85]}
\define\Indef{Werschulz~[86a]}
\define\IllPosed{Werschulz~[86b]}
\define\Fembad{Werschulz~[87a]}
\define\AprilAGW{Werschulz~[87b]}
\define\Resid{Werschulz~[87c]}
\define\Zen{Zeni\v sek~[72]}
DataMuseum.dk

DKUUG/EUUG Conference tapes

⟦1316cd710⟧ TextFile

Derivation

TextFile
