Computing Low-Rank Approximation of a Dense Matrix on Multicore CPUs with a GPU and Its Application to Solving a Hierarchically Semiseparable Linear System of Equations

Algorithm 1

Blocked QR factorization algorithm.

setup: and

while   do

  (1) panel factorization:

  for   do

    generation of Householder transformation:

    such that .

    right-looking update of panel:

   .

  end for

  (2) computation of matrix   :

  for   do

  end for

  (3) right-looking update of trailing submatrix:

  .

   and .

end while