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diff --git a/homeworks/hw-7.org b/homeworks/hw-7.org index e18d1ee..2c28af2 100644 --- a/homeworks/hw-7.org +++ b/homeworks/hw-7.org @@ -1,4 +1,4 @@ -#+TITLE: Homework 6 +#+TITLE: Homework 7 #+AUTHOR: Elizabeth Hunt #+LATEX_HEADER: \notindent \notag \usepackage{amsmath} \usepackage[a4paper,margin=1in,portrait]{geometry} #+LATEX: \setlength\parindent{0pt} @@ -58,4 +58,19 @@ See also the entry ~Eigen-Adjacent -> partition_find_eigenvalues~ in the LIZFCM documentation. * Question Six +Consider we have the results of two methods developed in this homework: ~least_dominant_eigenvalue~, and ~dominant_eigenvalue~ +into ~lambda_0~, ~lambda_n~, respectively. Also assume that we have the method implemented as we've introduced, +~shift_inverse_power_eigenvalue~. +Then, we begin at the midpoint of ~lambda_0~ and ~lambda_n~, and compute the +~new_lambda = shift_inverse_power_eigenvalue~ +with a shift at the midpoint, and some given initial guess. + +1. If the result is equal (or within some tolerance) to ~lambda_n~ then the closest eigenvalue to the midpoint + is still the dominant eigenvalue, and thus the next most dominant will be on the left. Set ~lambda_n~ + to the midpoint and reiterate. +2. If the result is greater or equal to ~lambda_0~ we know an eigenvalue of greater or equal magnitude + exists on the right. So, we set ~lambda_0~ to this eigenvalue associated with the midpoint, and + re-iterate. +3. Continue re-iterating until we hit some given maximum number of iterations. Finally we will return + ~new_lambda~. |