Computing the Matrix Cosine

  title={Computing the Matrix Cosine},
  author={Nicholas J. Higham and Matthew I. Smith},
  journal={Numerical Algorithms},
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
11 Citations
19 References
Similar Papers


Publications referenced by this paper.
Showing 1-10 of 19 references

An algorithm for computing the matrix cosine

  • S. M. Serbin, S. A. Blalock
  • SIAM J. Sci. Statist. Comput. 1(2)
  • 1980
Highly Influential
4 Excerpts

– Parlett algorithm for computing matrix functions

  • P. I. Davies, N. J. Higham, A Schur
  • 2002

LAPACK Users’ Guide

  • E. Anderson, Z. Bai, +8 authors D. C. Sorensen
  • 3rd ed.
  • 1999
2 Excerpts

Elementary Functions: Algorithms and Implementation (Birkhäuser

  • J.-M. Muller
  • 1997


  • G. A. Baker
  • and P. Graves-Morris, Padé Approximants…
  • 1996
1 Excerpt

Similar Papers

Loading similar papers…