\relax \bibstyle{plain} \@writefile{toc}{\contentsline {section}{\numberline {1}Overview}{4}} \newlabel{chapter:overview}{{1}{4}} \@writefile{toc}{\contentsline {section}{\numberline {2}Serial Solution of $A X = Y$ using an $LU$ factorization}{6}} \newlabel{section:LU-serial}{{2}{6}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Reading the input parameters}{6}} \newlabel{subsection:serial:input-data}{{2.1}{6}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Communicating the data for the problem}{6}} \newlabel{subsection:serial:communicating-data}{{2.2}{6}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.3}Reordering the linear system}{9}} \newlabel{subsection:serial:reordering}{{2.3}{9}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.4}Non-numeric work}{9}} \newlabel{subsection:serial:non-numeric}{{2.4}{9}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.5}The Matrix Factorization}{10}} \newlabel{subsection:serial:factor}{{2.5}{10}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.6}The Forward and Backsolves}{11}} \newlabel{subsection:serial:solve}{{2.6}{11}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.7}Sample Matrix and Right Hand Side Files}{12}} \newlabel{subsection:serial:input-files}{{2.7}{12}} \@writefile{toc}{\contentsline {section}{\numberline {3}Multithreaded Solution of $A X = Y$ using an $LU$ factorization}{13}} \newlabel{section:LU-MT}{{3}{13}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Reading the input parameters}{13}} \newlabel{subsection:MT:input-data}{{3.1}{13}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Communicating the data for the problem}{13}} \newlabel{subsection:MT:communicating-data}{{3.2}{13}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.3}Reordering the linear system}{13}} \newlabel{subsection:MT:reordering}{{3.3}{13}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.4}Non-numeric work}{13}} \newlabel{subsection:MT:non-numeric}{{3.4}{13}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.5}The Matrix Factorization}{14}} \newlabel{subsection:MT:factor}{{3.5}{14}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.6}The Forward and Backsolves}{15}} \newlabel{subsection:MT:solve}{{3.6}{15}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.7}Sample Matrix and Right Hand Side Files}{15}} \newlabel{subsection:MT:input-files}{{3.7}{15}} \@writefile{toc}{\contentsline {section}{\numberline {4}MPI Solution of $A X = Y$ using an $LU$ factorization}{16}} \newlabel{section:LU-MPI}{{4}{16}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.1}Reading the input parameters}{16}} \newlabel{subsection:MPI:input-data}{{4.1}{16}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.2}Communicating the data for the problem}{16}} \newlabel{subsection:MPI:communicating-data}{{4.2}{16}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.3}Reordering the linear system}{16}} \newlabel{subsection:MPI:reordering}{{4.3}{16}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.4}Non-numeric work}{17}} \newlabel{subsection:MPI:non-numeric}{{4.4}{17}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.5}The Matrix Factorization}{18}} \newlabel{subsection:MPI:factor}{{4.5}{18}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.6}The Forward and Backsolves}{19}} \newlabel{subsection:MPI:solve}{{4.6}{19}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.7}Sample Matrix and Right Hand Side Files}{20}} \newlabel{subsection:MPI:input-files}{{4.7}{20}} \@writefile{toc}{\contentsline {section}{\numberline {5}Serial Solution of $A X = Y$ using an $QR$ factorization}{21}} \newlabel{section:QR-serial}{{5}{21}} \@writefile{toc}{\contentsline {subsection}{\numberline {5.1}Reading the input parameters}{21}} \newlabel{subsection:QR:input-data}{{5.1}{21}} \@writefile{toc}{\contentsline {subsection}{\numberline {5.2}Communicating the data for the problem}{21}} \newlabel{subsection:QR:communicating-data}{{5.2}{21}} \@writefile{toc}{\contentsline {subsection}{\numberline {5.3}Reordering the linear system}{21}} \newlabel{subsection:QR:reordering}{{5.3}{21}} \@writefile{toc}{\contentsline {subsection}{\numberline {5.4}Non-numeric work}{21}} \newlabel{subsection:QR:non-numeric}{{5.4}{21}} \@writefile{toc}{\contentsline {subsection}{\numberline {5.5}The Matrix Factorization}{22}} \newlabel{subsection:QR:factor}{{5.5}{22}} \@writefile{toc}{\contentsline {subsection}{\numberline {5.6}Solving the linear system}{23}} \newlabel{subsection:QR:solve}{{5.6}{23}} \@writefile{toc}{\contentsline {subsection}{\numberline {5.7}Sample Matrix and Right Hand Side Files}{23}} \newlabel{subsection:QR:input-files}{{5.7}{23}} \@writefile{toc}{\contentsline {section}{\numberline {A}{\tt allInOne.c} -- A Serial $LU$ Driver Program}{24}} \newlabel{section:LU-serial-driver}{{A}{24}} \@writefile{toc}{\contentsline {section}{\numberline {B}{\tt allInOne.c} -- A Serial $LU$ Driver Program}{31}} \newlabel{section:LU-MT-driver}{{B}{31}} \@writefile{toc}{\contentsline {section}{\numberline {C}{\tt allInOne.c} -- A Serial $LU$ Driver Program}{39}} \newlabel{section:LU-MPI-driver}{{C}{39}} \@writefile{toc}{\contentsline {section}{\numberline {D}{\tt allInOne.c} -- A Serial $QR$ Driver Program}{49}} \newlabel{section:QR-serial-driver}{{D}{49}}