Superoptimal Preconditioners for Functions of Matrices

  title={Superoptimal Preconditioners for Functions of Matrices},
  author={Zhengjian Bai and Xiao-Qing Jin and Teng-Teng Yao},
  journal={Numerical Mathematics-theory Methods and Applications},
For any given matrix A ∈ C, a preconditioner tU (A) called the superoptimal preconditioner was proposed in 1992 by Tyrtyshnikov. It has been shown that tU (A) is an efficient preconditioner for solving various structured systems, for instance, Toeplitz-like systems. In this paper, we construct the superoptimal preconditioners for different functions of matrices. Let f be a function of matrices from C to C. For any A ∈ C, one may construct two superoptimal preconditioners for f(A): tU (f(A)) and… 

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