@techreport{NA-07/17,
  abstract = "New methods are proposed for the numerical evaluation of&nbsp;<em>f</em>(<strong>A</strong>)$ or&nbsp;<em>f</em>(<strong>A</strong>)&nbsp;<em>b</em>, where&nbsp;<em>f</em>(<strong>A</strong>) is a function such as&nbsp;<strong>A</strong><sup>&frac12;</sup>&nbsp;or log(<strong>A</strong>) with singularities in (-&infin;,0] and&nbsp;<strong>A</strong>&nbsp;is a matrix with eigenvalues on or near (0,&infin;). The methods are based on combining contour integrals evaluated by the periodic trapezoid rule with conformal maps involving Jacobi elliptic functions. The convergence is geometric, so that the computation of&nbsp;<em>f</em>(<strong>A</strong>)<em>b</em>&nbsp;is typically reduced to one or two dozen linear system solves, which can be carried out in parallel.",
  author = "Nicholas Hale and Nicholas J Higham and Lloyd N Trefethen",
  institution = "Oxford University Computing Laboratory",
  month = "August",
  number = "NA-07/17",
  title = "Computing A^{\alpha}, log(A) and related matrix functions by contour integrals",
  year = "2007",
}