Four Short Stories about Toeplitz Matrix Calculations −

  title={Four Short Stories about Toeplitz Matrix Calculations −},
  author={Thomas Strohmer},
Abstract. The stories told in this paper are dealing with the solution of finite, infinite, and biinfinite Toeplitz-type systems. A crucial role plays the off-diagonal decay behavior of Toeplitz matrices and their inverses. Classical results of Gelfand et al. on commutative Banach algebras yield a general characterization of this decay behavior. We then derive estimates for the approximate solution of (bi)infinite Toeplitz systems by the finite section method, showing that the approximation… CONTINUE READING
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