SUMMARY
The discussion focuses on efficiently computing eigenvalues and eigenvectors of a sparse penta-diagonal matrix representing a Hamiltonian. The user initially utilized the LAPACK routine dsyev for symmetric matrices but switched to dsbev for symmetric band matrices without significant improvement due to the distance of the outer bands. Recommendations include exploring the ARPACK library, although its documentation poses challenges. The consensus is that LAPACK is suitable for banded matrices, but may not fully leverage sparsity in this specific case.
PREREQUISITES
- Understanding of Hamiltonian mechanics and matrix representation
- Familiarity with LAPACK routines, specifically dsyev and dsbev
- Knowledge of sparse matrix concepts and their computational advantages
- Basic proficiency in using ARPACK for eigenvalue problems
NEXT STEPS
- Research the implementation and usage of ARPACK for sparse eigenvalue problems
- Explore advanced LAPACK functionalities for banded matrices
- Study optimization techniques for sparse matrix computations
- Investigate alternative libraries for eigenvalue computations, such as Eigen or SLEPc
USEFUL FOR
Researchers, physicists, and computational mathematicians working with Hamiltonians and seeking efficient algorithms for eigenvalue problems in sparse banded matrices.