ISSN:
0945-3245
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary Without using spectral resolution, an elementary proof of convergence of Seidel iteration. The proof is based on the lemma (generalizing a lemma of P. Stein): If (A+A *)−B *(A+A *)B〉0, whereB=−(P+L) −1 R,A=P+L (Lower)+R (upper), then Seidel iteration ofAX=Y 0 converges if and only ifA+A *〉0. This lemma has as corollaries not only the well-known results of E. Reich and Stein, but also applications to a matrix that can be far from symmetric, e.g.M=[A ij ] 1 2 , whereA 21=−A 12 * ,A 11,A 22 are invertible;A 11 +A 11 * =A22+A 22 * ; and the proper values ofA 12 −1 A 11,A 12 *−1 A 22 are in the interior of the unit disk.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01395932
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