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			\contentsline {section}{Problem 1}{3}%
			\contentsline {subsection}{(1) Steepest Descent \& Conjugate Gradient}{3}%
			\contentsline {subsection}{(2) Heat Transport across a Square Platelet}{5}%
			\contentsline {subsection}{(3) The Nonlinear Conjugate Gradient Method}{6}%
			\contentsline {subsubsection}{Study of the configurations, $N = 2,3,4$}{7}%
			\contentsline {subsubsection}{Case $N = 5$}{8}%
			\contentsline {subsubsection}{Case $N = 6$}{10}%
			\contentsline {section}{Problem 2}{12}%
			\contentsline {subsection}{(1) Over defined system of linear equations}{12}%
			\contentsline {subsection}{(2) (SVD) decomposition }{12}%
			\contentsline {subsubsection}{Compressing images}{12}%
			\contentsline {subsubsection}{Ising model interpretation}{14}%
			\contentsline {subsection}{(3) SVD and quantum ground state compression}{15}%
			\contentsline {subsubsection}{Further analysis and the translation symmetry}{16}%