Abstract

REVERSE QUADRATIC ARNOLDI METHOD FOR THE SOLUTION OF QUADRATIC EIGENVALUE PROBLEMS

1Usman Sanusi & 2Hamisu Musa

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Abstract Quadratic Arnoldi (Q-Arnoldi) method is known to suffer from numerical instability (vectors spanning the Krylov subspace may lose orthogonality). In this paper we reversed the algorithm to target largest eigenvalues of the QEP. We call the algorithm Reverse Q-Arnoldi (RQ-Arnoldi). It was found that the reversion resulted to a numerically stable algorithm. The experiments carried out also showed that the RQ-Arnoldi does not lose orthogonality. Keywords: Quadratic Eigenvalue Problem, Q-Arnoldi Method, RQ-Arnoldi, Stability, Instability.

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