Skip to content

Correct asymptotic runtime of SVD #58

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Open
charmoniumQ wants to merge 1 commit into
base: main
Choose a base branch
from
Open

Correct asymptotic runtime of SVD #58

Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
4 changes: 1 addition & 3 deletions notes/svd.md
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -135,9 +135,7 @@ $$\mathbf{A}^T\mathbf{A}(\mathbf{A}^T\mathbf{x}) = \lambda (\mathbf{A}^T\mathbf{

## Time Complexity

The time-complexity for computing the SVD factorization of an arbitrary \\(m \times n\\) matrix is $$\alpha (m^2n + n^3)$$, where the constant $$\alpha$$ ranges from 4 to 10 (or more) depending on the algorithm.

In general, we can define the cost as: $$\mathcal{O}(m^2n + n^3)$$
The number of floating-point operations used when computing the SVD factorization of an arbitrary \\(m \times n\\) matrix is $$\alpha (mn^2 + n^3)$$, where the constant $$\alpha$$ ranges from 4 to 10 (or more) depending on the algorithm. Thus, for square matrices, we have an algorithmic complexity of $$\mathcal{O}(n^3)$$.

<div class="figure"> <img src="{{ site.baseurl }}/assets/img/figs/svd_graph.png" height=300 width=600/> </div>

Expand Down