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lizfcm/homeworks/hw-8.org
Elizabeth Hunt b5ad184c1b
hw8 checkpoint
2023-12-08 09:21:32 -07:00

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Homework 7

TODO: Update LIZFCM org file with jacobi solve, format_matrix_into, rand

Question One

See UTEST(jacobi, solve_jacobi) in test/jacobi.t.c and the entry Jacobi -> solve_jacobi in the LIZFCM API documentation.

Question Two

A problem arises when using the Jacobi method to solve for the previous population distribution, $n_k$, from $Ln_{k} = n_{k+1}$, because a Leslie matrix is not diagonally dominant and will cause a division by zero. Likewise, we cannot factor it into $L$ and $U$ terms and apply back substitution because pivot points are zero.

Question Three