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-\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}%