TY  - JOUR
AB  - We develop the theory of convergence of a generic GR algorithm for the matrix eigenvalue problem that includes the QR,LR,SR, and other algorithms as special cases. Our formulation allows for shifts of origin and multiple GR steps. The convergence theory is based on the idea that the GR algorithm performs nested subspace iteration with a change of coordinate system at each step. Thus the convergence of the GR algorithm depends on the convergence of certain sequences of subspaces. It also depends on the quality of the coordinate transformation matrices, as measured by their condition numbers. We show that with a certain obvious shifting strategy the GR algorithm typically has a quadratic asymptotic convergence rate. For matrices possessing certain special types of structure, cubic convergence can be achieved.
DA  - 1991
DO  - 10.1016/0024-3795(91)90004-G
LA  - eng
M2  - 19
PY  - 1991
SN  - 0024-3795
SP  - 19-47
T2  - Linear algebra and its applications
TI  - Convergence of algorithms of decomposition type for the eigenvalue problem
UR  - https://nbn-resolving.org/urn:nbn:de:0070-pub-17808343
Y2  - 2024-11-22T08:44:13
ER  -