Chapter 5
Summary
The development and implementation of efficient methods for solving banded eigenproblems on high-performance architectures is one of the challenging problems in numerical linear algebra.
This report points out new ways towards highly efficient and numerically stable eigensolvers for band matrices. The goal is to overcome difficulties which have been faced in previous attempts.
Algorithmic aspects of the new method are discussed in an accompanying report (Gansterer et al. [16]). Numerical aspects and implementation details are discussed in a forthcoming report.