A quadratically convergent QR-like method without shifts for the Hermitian eigenvalue problem (Q2502892)

The authors study the classical Hermitian eigenvalue problem \(Ax=\lambda x\) from a nonclassical point of view. Instead of improving the convergence properties of some of the well-known methods which grow the powers of \(A\) linearly, the authors propose a new algorithm which converges quadratically without using any kind of shifts. A rigorous convergence analysis is provided, in order to cover also the case where \(A\) has clusters of eigenvalues. Moreover the algorithm can be easily parallelized. After some well-built examples, an effective last section points out some present weaknesses of the proposed algorithm and some possible improvements.