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 5
QRP factorization and postprocessing algorithms, where condest computes an estimation of the condition number of .
(a)
QPR factorization algorithm.
(1) QR factorization with restricted pivoting:
setup: and .
While do
(1.1) panel factorization:
setup: initialize column norms within the window,
(last column in window).
for do
(1.1.1) restricted pivoting:
swap th column with pivot column
of the largest norm within the window.
if condestthen
and break.
(update numerical rank).
(1.1.2) Householder matrix computation:
.
(1.1.3) right-look update of window:
.
end for
(1.2) trailing submatrix update: ().
compute matrix .
update trailing submatrix right of current window.
