Scientific Programming / 2015 / Article / Alg 2

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 2

QP3 factorization algorithm, where is the submatrix consisting of the th and th columns of .
setup: Compute the column norms
    for   , and .
While   do
   (1) panel factorization:
  for   do
    (1.1) pivoting:
       select the pivot column with the largest .
        and .
       .
        (update numerical rank).
    (1.2) left-looking update of pivot column:
       .
    (1.3) Householder matrix computation:
        such that .
    (1.4) Computation of the -auxiliary vector :
       
    (1.5) right-look update of pivot row:
       
    (1.6) norm downdate:
        for .
        (if norms must be recomputed then break)
  end for
   (2) trailing submatrix update:
  .
   (recompute norms if necessary).
end while

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