Conjugate gradient methods for the Rayleigh quotient minimization of generalized eigenvalue problems. (English) Zbl 0788.65043

For the computation of extreme eigenvalues and corresponding eigenvectors of the generalized eigenvalue problem \(Ax= \lambda Bx\), where \(A\) is real symmetric and \(B\) is positive definite, the conjugate gradient method for minimization of the Rayleigh quotient by W. W. Bradbury and R. Fletcher [New iterative methods for solution of the eigenproblem. Numer. Math. 9, 259-267 (1966; Zbl 0202.435)] is discussed and modified. The author considers proper step sizes in the one-dimensional minimization of the Rayleigh quotient and discusses properties, in particular, the convergence of the modified conjugate gradient methods for the generalized eigenvalue problem.
Reviewer: Z.Mei (Toowoomba)


65F15 Numerical computation of eigenvalues and eigenvectors of matrices


Zbl 0202.435
Full Text: DOI


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