The MKL manual mentions routines to calculate the complete set of eigenvalues of a full matrix. I understand that intel has worked at optimizing the calculation of subsets of eigenvalues for sparse matrices.
Question: Are there routines to evaluate just a subset of eigenvalues, e.g. largest, smallest, positive real part, etc, for full matrices (without sparsifying the matrix)?
Check out https://software.intel.com/en-us/mkl-developer-reference-c-lapack-least-squares-and-eigenvalue-problem-routines. Dense matrices are covered by BLAS and LAPACK routines and MKL has a plenty of functionality for solving eigenproblems in LAPACK component.
E.g., have a look at https://software.intel.com/en-us/mkl-developer-reference-c-stemr#9EE784BD-3C06-420A-8AE0-AE93C2E1B830