Optimizing Halley's Iteration for Computing the Matrix Polar Decomposition

نویسندگان

  • Yuji Nakatsukasa
  • Zhaojun Bai
  • François Gygi
چکیده

We introduce a dynamically weighted Halley (DWH) iteration for computing the polar decomposition of a matrix, and prove that the new method is globally and asymptotically cubically convergent. For matrices with condition number no greater than 1016, the DWH method needs at most 6 iterations for convergence with the tolerance 10−16. The Halley iteration can be implemented via QR decompositions without explicit matrix inversions. Therefore, it is an inverse free communication friendly algorithm for the emerging multicore and hybrid high performance computing systems.

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عنوان ژورنال:
  • SIAM J. Matrix Analysis Applications

دوره 31  شماره 

صفحات  -

تاریخ انتشار 2010