ABLE: An adaptive block Lanczos method for non-Hermitian eigenvalue problems

This work presents an adaptive block Lanczos method for large-scale non-Her mitian Eigenvalue problems (henceforth the ABLE method). The ABLE method is a block version of the non-Hermitian Lanczos algorithm. There are three in novations. First, an adaptive blocksize scheme cures (near) breakdown and a dapts the blocksize to the order of multiple or clustered eigenvalues. Seco nd, stopping criteria are developed that exploit the semiquadratic converge nce property of the method. Third, a well-known technique from the Hermitia n Lanczos algorithm is generalized to monitor the loss of biorthogonality a nd maintain semibiorthogonality among the computed Lanczos vectors. Each in novation is theoretically justified. Academic model problems and real appli cation problems are solved to demonstrate the numerical behaviors of the me thod.