# the algorithm and computation cost for truncated SVD in rank k

It seems that the time cost of truncated SVD in rank k for matrix $A\in R^{m\times m}$ is $O(m^2 k)$. Could anyone show me some algorithms to calculate truncated SVD with the above time complexity?

• There is the svds function in Matlab which might a bit cheaper than the full SVD but it might be less accurate than calculating TSVD from the full SVD. Mar 6, 2015 at 13:24
• There are a number of details that are needed to answer such a question well. First, is $A$ sparse or dense? Second, how much smaller is $k$ vs $m$? Finally, what will you be using the truncated SVD for? Mar 6, 2015 at 21:11