# Why is LAPACK (seemingly) suboptimal for packed and banded eigenvalue problems?

Based on this LAPACK routines list, it looks like there is no relatively robust representation (RRR) driver routine for either packed or banded symmetric eigenvalue problems. According to the relevant LAPACK documentation though, it appears that the RRR driver is the fastest algorithm in most cases and uses the least workspace. Furthermore, based on the method used by LAPACK for symmetric eigenvalue problems, LAPACK tridiagonalizes the given matrix for all cases (full, packed, banded) and then runs an appropriate routine (RRR or otherwise) on the symmetric tridiagonal matrix thus yielded.

So this raises the question: if RRR is typically the most efficient routine, and it can (seemingly?) work for packed and banded matrices (since it works on symmetric tridiagonal matrices), why is there no RRR driver routine for packed or banded matrices?

(And if there is no good reason, would it be potentially more efficient for a user to tridiagonalize themselves using the computational routine *btrd and then call the driver routine stevr on the symmetric tridiagonal matrix thus yielded?)

• Cross-posted on StackOverflow – Anton Menshov Jun 14 '20 at 4:03
• @AntonMenshov Should I delete the SO one? I originally was not sure where it would be most useful to post. – Grayscale Jun 14 '20 at 4:20
• Grayscale, I would not do it for this particular question right now. I just want to make sure there is a link here. See this for reference. – Anton Menshov Jun 14 '20 at 5:58