On the Convergence of Iterative Orthogonalization Processes
- 1 March 1976
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Aerospace and Electronic Systems
- Vol. AES-12 (2) , 146-151
- https://doi.org/10.1109/taes.1976.308289
Abstract
Polar decomposition of matrices is used here to investigate the convergence properties of iterative orthogonalization processes. It is shown that, applying this decomposition, the investigation of a general iterative process of a certain form can be reduced to the investigation of a scalar iterative process which is simple. Three known iterative orthogonalization processes, which are special cases of the general process, are analyzed, their convergence rate (order) is determined, and their range of convergence is established in terms of the spectral radius of the modulus of the matrix which is being orthogonalyzed.Keywords
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