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The ILU-based preconditioning methods in previous work have their ownparameters to improve their performances. Although the parameters may degradethe performance, their determination is left to users. Thus, these previousmethods are not reliable in practical computer-aided engineering use. Thispaper proposes a novel ILU-based preconditioner called the auto-acceleratedILU, or A2ILU. In order to improve the convergence, A2ILU introducesacceleration parameters which modify the ILU factorized preconditioning matrix.A$^2$ILU needs no more operations than the original ILU because theacceleration parameters are optimized automatically by A2ILU itself. Numericaltests reveal the performance of A2ILU is superior to previous ILU-based methodswith manually optimized parameters. The numerical tests also demonstrate theability to apply auto-acceleration to ILU-based methods to improve theirperformances and robustness of parameter sensitivities.

A2ILU: Auto-accelerated ILU Preconditioner for Sparse Linear Systems