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 3

Unification principle of QRP algorithm.

(a)

Golub algorithm for task-1.

for   do

  Golub-I

end for

(b)

Chan algorithm for task-2.

for   do

  Chan-II

end for

(c)

Golub-I algorithm.

(1) compute the column norms:

   for

(2) find a pivot column such that

(3) shift columns for column pivot:

   for

(4) re-triangularize :

   for   do

   (4.1) generate a Given's rotation

       to zero out with

   (4.2) apply the Given's rotation

       to the trailing submatrix

   end for

(d)

Chan-II algorithm.

(1) compute right singular vector

  corresponding to

(2) find a pivot column such that

(3) shift columns for column pivot:

  for

(4) re-triangularize :

   for   do

  (4.1) generate a Given's rotation

      to zero out with

  (4.2) apply the Given's rotation

      to the trailing submatrix

end for