Arnoldi algorithm

We use the Arnoldi algorithm of the ARPACK[14] libraries which is the implementation of implicitly restarted Lanezos method (IRLM) of Sorensen[17]. The... 

Non-variational calculations of the excited acceptor states in cubic compound semiconductors using the finite element method and Arnoldi algorithm have also been performed, with application to some II—VI and III—V compounds [51,52]. The nS3/2 states (n = 1 to 8) have been calculated in the spherical approximation for //, varying between 0 and 0.95 in steps of 0.05 while the nP3/2 (r3), nP5/2 (r3) and nP5/2 7) states (n = 2 to 5) have been calculated including the cubic term 6 (6 = 0.05 and 0.15) for the same domain of variation of /. The case of the single and double acceptors in GaAs has been specifically studied by Fiorentini [18]. A discussion of the results of these calculations will be presented in relation to the experimental data. 

Note also that for a generic linear generator A such as that of CODDE (Sec. 2.3), the Lanczos or Arnoldi algorithm results in an upper Hessenberg matrix such that [45, 46, 52]... 

R. Sureshkumar and A.N. Beris, Linear stability of viscoelastic Poiseuille flow using an Arnoldi based orthogonalisation algorithm, J. Non-Newtonian Fluid Mech., 56 (1995) 151-182. 

Arnoldi-based algorithm is a classical Krylov-subspace-based Model Order Reduction technique. It reduces the dimension of the spatially semi-discretized form of the original governing PDEs using moment-matching of transfer functions. 

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