Solution of eigenvalue problems in Hilbert spaces by a gradient method

✍ Scribed by E.K. Blum; G.H. Rodrigue

• Publisher: Elsevier Science
• Year: 1974
• Tongue: English
• Weight: 664 KB
• Volume: 8
• Category: Article
• ISSN: 0022-0000
• DOI: 10.1016/s0022-0000(74)80056-5

✦ Synopsis

A gradient technique is developed for computing a class of nonisolated stationary points, called C-stationary points, for a real functional F defined on a Hilbert space. It is shown that the least-squares solutions of the operator equation Ax = b are C-stationary points for the functional (1/2)IJ Ax -b [] 2 when R(A) is closed and that certain eigenvectors of the general eigenproblem Ax = ,UBx are C-stationary points for the functional 89 I[ Ax --((Ax, Bx)/(Bx, Bx)) Bx II ~. Numerical experiments are given to justify the results.