Computational & Applied Mathematics
On-line version ISSN 1807-0302
PINTO DA COSTA, A. and SEEGER, Alberto. Numerical resolution of cone-constrained eigenvalue problems. Comput. Appl. Math. [online]. 2009, vol.28, n.1, pp. 37-61. ISSN 1807-0302. http://dx.doi.org/10.1590/S0101-82052009000100003.
Given a convex cone K and matrices A and B, one wishes to find a scalar λ and a nonzero vector x satisfying the complementarity system K ∋ x ⊥(Ax-λ Bx) ∈ K+. This problem arises in mechanics and in other areas of applied mathematics. Two numerical techniques for solving such kind of cone-constrained eigenvalue problem are discussed, namely, the Power Iteration Method and the Scaling and Projection Algorithm.
Keywords : complementarity condition; generalized eigenvalue problem; power iteration method; scaling; projection algorithm.