\babel@toc {english}{}\relax 
\contentsline {chapter}{\numberline {1}Introduction}{1}{chapter.1}%
\contentsline {chapter}{\numberline {2}Problem Definition}{2}{chapter.2}%
\contentsline {section}{\numberline {2.1}QR}{2}{section.2.1}%
\contentsline {section}{\numberline {2.2}L-BFGS}{3}{section.2.2}%
\contentsline {section}{\numberline {2.3}Conditioning}{4}{section.2.3}%
\contentsline {chapter}{\numberline {3}Algorithms}{6}{chapter.3}%
\contentsline {section}{\numberline {3.1}QR}{6}{section.3.1}%
\contentsline {section}{\numberline {3.2}L-BFGS}{8}{section.3.2}%
\contentsline {chapter}{\numberline {4}Experiments}{12}{chapter.4}%
\contentsline {section}{\numberline {4.1}QR}{13}{section.4.1}%
\contentsline {section}{\numberline {4.2}L-BFGS}{14}{section.4.2}%
\contentsline {section}{\numberline {4.3}Comparison between QR and L-BFGS}{15}{section.4.3}%
\contentsline {section}{\numberline {4.4}Other Experiments}{17}{section.4.4}%
\contentsline {subsection}{\numberline {4.4.1}The Effect of the Memory Size}{17}{subsection.4.4.1}%
\contentsline {subsection}{\numberline {4.4.2}A Comparison of Quasi-Newton Methods}{18}{subsection.4.4.2}%
\contentsline {chapter}{\numberline {5}Concluding Remarks}{21}{chapter.5}%
\contentsline {chapter}{\numberline {6}Proofs}{22}{chapter.6}%