Tamtam Proceedings - lamsin

¨§¨ §IRAM method 509To overcome these limitations, two solutions are suggested in the litterature (cf. [3], [4]).We can increase m, since bigger is m, better the eigenpairs of H m approximate those of Aand greater is our chance in finding the desired eigenpairs among those of H m . In the limitcase of m = n, the Arnoldi method is identified to the classical QR method (cf. [3], [4]).In the particular case of large-scale sparse matrices and if we are interested in only feweigenpairs, larger values of m implies more storage space is needed, a deterioration of thenumerical stability, and an increase in computation cost. Another alternative is suggested,which consists on re-initializing the starting vector v 0 , without increasing m. This can bedone either explicitly or implicitly, as illustrated in the following.2.2. The Implicitly Restarted Arnoldi MethodFor large eigenvalue problems which arise in many engineering contexts, the desiredeigenvalues have generally some particular features. For example, the user may requirethe k eigenvalues of largest real part, or the k eigenvalues nearest a point in the complexplane, with k