\relax \newlabel{eqn:stationary}{{2.1}{xix}} \newlabel{eqn:ith-equation}{{2.2}{xxvii}} \newlabel{eqn:jacobi-pointwise}{{2.3}{xxviii}} \newlabel{eqn:jacobi-matrixwise}{{2.4}{xxix}} \@writefile{lof}{\string\contentsline\space {figure}{\string\numberline\space {2.1}{\ignorespaces The Jacobi Method}}{xxxvi}} \newlabel{fig:jacobi}{{2.1}{xxxvi}} \newlabel{eqn:gauss-seidel-pointwise}{{2.5}{lv}} \newlabel{eqn:gauss-seidel-matrixwise}{{2.6}{lvii}} \@writefile{lof}{\string\contentsline\space {figure}{\string\numberline\space {2.2}{\ignorespaces The Gauss-Seidel Method}}{lviii}} \newlabel{fig:gs}{{2.2}{lviii}} \newlabel{eqn:sor-matrix}{{2.7}{lxi}} \@writefile{lof}{\string\contentsline\space {figure}{\string\numberline\space {2.3}{\ignorespaces The SOR Method}}{lxii}} \newlabel{fig:sor}{{2.3}{lxii}} \newlabel{eqn:sta:optimal:omega}{{2.8}{lxxvii}} \newlabel{eqn:ssor-matrix}{{2.9}{lxxviii}} \@writefile{lof}{\string\contentsline\space {figure}{\string\numberline\space {2.4}{\ignorespaces The SSOR Method}}{lxxxiv}} \newlabel{fig:ssor}{{2.4}{lxxxiv}} \newlabel{eqn:cg:res-update}{{2.10}{xc}} \newlabel{eqn:cg:dir-update}{{2.11}{xciv}} \@writefile{lof}{\string\contentsline\space {figure}{\string\numberline\space {2.5}{\ignorespaces The Preconditioned Conjugate Gradient Method}}{cx}} \newlabel{fig:pcg}{{2.5}{cx}} \newlabel{cg_cond}{{2.12}{cxxvi}} \@writefile{lof}{\string\contentsline\space {figure}{\string\numberline\space {2.6}{\ignorespaces The Preconditioned GMRES$(m)$ Method}}{clxix}} \newlabel{fig:pgmres}{{2.6}{clxix}} \@writefile{lof}{\string\contentsline\space {figure}{\string\numberline\space {2.7}{\ignorespaces The Preconditioned BiConjugate Gradient Method}}{clxxiv}} \newlabel{fig:pbcg}{{2.7}{clxxiv}} \@writefile{lof}{\string\contentsline\space {figure}{\string\numberline\space {2.8}{\ignorespaces The Preconditioned Quasi Minimal Residual Method without Look-ahead}}{clxxix}} \newlabel{fig:pqmr}{{2.8}{clxxix}} \newlabel{eqn:cgs}{{2.13}{clxxxviii}} \newlabel{eqn:cgs2}{{2.14}{cxc}} \@writefile{lof}{\string\contentsline\space {figure}{\string\numberline\space {2.9}{\ignorespaces The Preconditioned Conjugate Gradient Squared Method}}{cxcv}} \newlabel{fig:pcgs}{{2.9}{cxcv}} \@writefile{lof}{\string\contentsline\space {figure}{\string\numberline\space {2.10}{\ignorespaces The Preconditioned BiConjugate Gradient Stabilized Method}}{cci}} \newlabel{fig:pbcgstab}{{2.10}{cci}} \newlabel{eqn:minr}{{2.15}{ccvii}} \@writefile{lof}{\string\contentsline\space {figure}{\string\numberline\space {2.11}{\ignorespaces The Preconditioned Chebyshev Method}}{ccxx}} \newlabel{fig:pcheby}{{2.11}{ccxx}} \@writefile{lot}{\string\contentsline\space {table}{\string\numberline\space {2.1}{\ignorespaces Summary of Operations for Iteration\penalty \@M \ $i$. ``a/b'' means ``a'' multiplications with the matrix and ``b''\penalty \@M \ with its transpose.}}{ccxxiii}} \newlabel{perf_ops_tbl}{{2.1}{ccxxiii}} \@writefile{lot}{\string\contentsline\space {table}{\string\numberline\space {2.2}{\ignorespaces Storage Requirements for the Methods in iteration\penalty \@M \ $i$: $n$\penalty \@M \ denotes the order of the matrix.}}{ccxxiv}} \newlabel{store_tbl}{{2.2}{ccxxiv}} \newlabel{sparseA}{{4.1}{dxxii}} \newlabel{sparseA2}{{4.2}{dxl}} \newlabel{eqn:diag-conversion}{{4.3}{dxli}} \newlabel{sparseA3}{{4.4}{dlv}} \@writefile{lof}{\string\contentsline\space {figure}{\string\numberline\space {4.1}{\ignorespaces Profile of a nonsymmetric skyline or variable-band matrix.}}{dlxiv}} \newlabel{sec:data-structures.skyline}{{4.1}{dlxiv}} \@writefile{lof}{\string\contentsline\space {figure}{\string\numberline\space {4.2}{\ignorespaces A rearrangement of Conjugate Gradient for parallelism}}{dcix}} \newlabel{fig:rearrangedcg}{{4.2}{dcix}} \newlabel{proj}{{5.1}{dcliii}} \newlabel{redblk}{{5.2}{dclxiii}} \newlabel{rs}{{5.3}{dclxix}} \newlabel{prob}{{5.4}{dclxxvi}} \newlabel{block-eqn1}{{5.5}{dccxxxv}} \newlabel{block-eqn2}{{5.6}{dccxxxviii}} \newlabel{SB-eqn}{{5.7}{dccxliii}} \newlabel{BPS-part}{{5.8}{dccliii}} \newlabel{SB-block}{{5.9}{dcclxiv}} \newlabel{BPS-def1}{{5.10}{dcclxxx}} \newlabel{VS-def1}{{5.11}{dccxciv}}