HÄuper Knut. A Calculus Approach to Matrix Eigenvalue Algorithms. Habilitationsschrift

HÄuper Knut. A Calculus Approach to Matrix Eigenvalue Algorithms. Habilitationsschrift. - WÄurzburg im Juli 2002 - 81 p.
der FakultÄat fÄur Mathematik und Informatik
der Bayerischen Julius-Maximilians-UniversitÄat WÄurzburg
fÄur das Fach Mathematik vorgelegt vonJacobi-type Algorithms and Cyclic Coordinate Descent
Algorithms
Jacobi and Cyclic Coordinate Descent
Block Jacobi and Grouped Variable Cyclic Coordinate
Descent
Applications and Examples for 1-dimensional Optimization
Applications and Examples for Block Jacobi
Local Convergence Analysis
Discussion
Refining Estimates of Invariant Subspaces
Lower Unipotent Block Triangular Transformations
Algorithms
Main Ideas
Formulation of the Algorithm
Further Insight to Orderings
Orthogonal Transformations
The Algorithm
Local Convergence Analysis
Discussion and Outlook
Rayleigh Quotient Iteration, QR-Algorithm, and Some Generalizations
Local Cubic Convergence of RQIParallel Rayleigh Quotient Iteration or Matrix-valued Shifted QR-Algorithms
Discussion
Local Convergence Properties of the Shifted QR-Algorithm