Efficient calculation of bounds on spectra of Hessian matrices. (English) Zbl 1181.65055

Mönnigmann, M.

SIAM J. Sci. Comput. 30, No. 5, 2340-2357 (2008).

The author deals with bounds on spectra of Hessian matrices of twice continuously differentiable functions that can be implemented as a codelist. A new approach for the calculation of eigenvalue bounds is proposed. The favorable complexity of the new approach results because the eigenvalue bounds can be found without ever calculating the Hessian matrix. Numerical results are presented to show that the proposed approach may result in bounds that are worse or better than Gershgorin’s bounds, but the complexity is one order less.

Reviewer: Liu Xinguo (Qingdao)

MSC:

65F15	Numerical computation of eigenvalues and eigenvectors of matrices
15A42	Inequalities involving eigenvalues and eigenvectors
65Y20	Complexity and performance of numerical algorithms

Keywords:

eigenvalue bounds; Hessian; elementary function evaluation; complexity; numerical results; Gershgorin’s bounds

Software:

INTOPT_90