March 3, 2026Open Access

On Complex Rotated Block Triangular Preconditioned Iteration Methods for a Class of Block Two-by-Two Complex Linear Systems

Key Points

The application of complex rotating block triangular preconditioners increases the efficiency of Krylov subspace methods, leading to faster convergence.
In comparing performance, these preconditioners show competitive results against the traditional BAS preconditioner—offering potentially better outcomes in similar settings.
Investigation into the spectrum characteristics of preconditioned matrices reveals significant advantages for optimal control problems involving periodic eddy current equations.
The study emphasizes that implementing these methods may lead to enhanced computational efficiency, particularly in complex linear systems.

Abstract

For the optimal control problems bound by the time-periodic eddy current equation, we build a class of complex rotating block triangular preconditioners based on the BAS preconditioning matrix. The corresponding preconditioned matrices' spectrum characteristics are examined. The application of these complicated rotated block triangular preconditioners to quicken Krylov subspace iteration techniques demonstrates their potential to be competitive with and even more effective than the BAS preconditioner.

On Complex Rotated Block Triangular Preconditioned Iteration Methods for a Class of Block Two-by-Two Complex Linear Systems

Key Points

Abstract

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