✦ LIBER ✦

The computation of eigenvalues and eigenvector of a completely continuous self-adjoint operator

✍ Scribed by E.K. Blum

Publisher: Elsevier Science
Year: 1967
Tongue: English
Weight: 307 KB
Volume: 1
Category: Article
ISSN: 0022-0000
DOI: 10.1016/s0022-0000(67)80026-6

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✦ Synopsis

If A is a completely continuous self-adjoint operator on a Hilbert space, its eigen= values are the values of the inner product (Ax, x) at stationary points on the unit sphere. Gradient procedures can be used to determine eigenvectors and eigenvalues provided that certain regularity conditions hold at the eigenvectors. It is proven that these conditions are satisfied at any eigenvector belonging to an eigenvalue of multiplicity one.

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