Scientific Programming / 2015 / Article / Alg 3

Research Article

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

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