Computing the Matrix Cosine

@article{Higham2003ComputingTM,
  title={Computing the Matrix Cosine},
  author={Nicholas J. Higham and Matthew I. Smith},
  journal={Numerical Algorithms},
  year={2003},
  volume={34},
  pages={13-26}
}
An algorithm is developed for computing the matrix cosine, building on a proposal of Serbin and Blalock. The algorithm scales the matrix by a power of 2 to make the ∞-norm less than or equal to 1, evaluates a Padé approximant, and then uses the double angle formula cos (2A)=2cos (A)2−I to recover the cosine of the original matrix. In addition, argument reduction and balancing is used initially to decrease the norm. We give truncation and rounding error analyses to show that an [8,8] Pad… CONTINUE READING
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