No, I don't think you can easily find the SVD of a subset of the rows of a matrix, based on the SVD of the full matrix. At least, not easily. (@Christine Tobler) may have an idea.
But whenever I see a question like this, I wonder if the real problem is, you are trying to solve the wrong problem. That is, one reason for computing the SVD repeatedly may be to find the numerical rank of each subset of the rows. Or maybe you want to find the subset of rows that are maximally independent from each other. And if you are doing something like one of these things, there are likely better ways of doing so than repeat calls to SVD.
It is often the case that someone asks a question, looking to make the scheme they have run faster, but the real issue is, you need to improve the approach you are taking. Find a better way of solving the problem than what you are doing.
Edit:
For example, if your goal is to find the subset of k rows of your matrix, such that the condition number of the resulting matrix is as small as possible, when you extract that set of rows and then compute the condition number on that subset? Now, rather than computing cond on EVERY subset of rows, I might try using GA. Have GA select the subset, with minimal condition number. Will this really gain? Well, yes. Consider this example:
A = rand(1e6,10);
Now, my goal is to find the subset of 10 rows from all 1e6 rows, such that the condition number is as small as possible. It might be a moderately interesting problem (though I have no idea if it is your real problem.) Were we to apply brute force, that would necessitate MATLAB to compute
nchoosek(1e6,10)
calls to COND (which calls SVD). And clearly that would be an insane thing to do. But we could use GA instead, to identify a subset of those rows, with a minimal condition number. Yes, GA might not find the perfectly optimal solution, but it would be massively better than anything you could do using brute force, and the result would take only some thousands of calls to COND. Even if it was many thousands of calls, you win by use of an optimization tool here.
Agin, I have no clue as to why you have decided to perform this programming task. Maybe someone told you to do it this way, or maybe you decided it was the way to solve some problem. But that does not make necessarily a good way to approach the real underlying problem. We don't know, because all we see is the final question that you think to be important.
