Optimized Structured Preconditioner for a Class of Complex Symmetric Linear Systems

Abstract

An optimized structured (OS) preconditioner for a class of complex symmetric linear systems is proposed. The OS-preconditioner results in a fast Krylov subspace solver, which is robust with respect to the mesh-size. The computational complexity of OS-preconditioner is analyzed and it is shown that all eigenvalues of the corresponding preconditioned matrix are positive real and distributed on[$\frac{1}{2}$+$\frac{\varepsilon }{{2\sqrt {1 + {\varepsilon ^2}} }}$,1]. Numerical experiments confirming the theoretical derivations are presented to verify the effectiveness and stability of the OS-preconditioner.