Claculating interior eigenvalues and eigenvectors with an implicitly restarted and a filter diagonalization method (Q5937473)

This is a comparison of two iterative methods for calculating eigenvalue/eigenvector pairs for real symmetric matrices. The authors calculated several hundred eigenvalues of matrices of sizes up to one million, motivated by problems on molecules in chemistry. In most cases they were unable to calculate interior eigenvalue/eigenvector pairs by the implicitly restarted method of \textit{J. Baglama}, \textit{D. Calvetti} and \textit{L. Reichel} [BIT 36, No. 3, 400-421 (1996; Zbl 0856.65030)], whereas they found the filter diagonalization method of \textit{Mandelstam} and \textit{Taylor} [J. Chem. Phys. 106, 5085 (1997)] ``extremely effective''. The \(C\) and \(W\)-Lanczos method and improvements are briefly mentioned.