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OpenATLib and Xabclib User's Manual for Version 1.0
3.2
OpenATI_DAFSTG
3.2.1
Overview of the function
Recently, many iterative solvers and preconditioner methods are proposed. However,
the
history of relative residual
shows the
various movements
by
solvers,
precondiotiners and matrices. Hence, we need to predict the solver will satisfy user’s
request or not from the history of relative residual so far.
OpenATI_DAFSTG enables us to detect the stagnation of relative residual from the
history of them.
3.2.2
Overview of the auto-tuning method
OpenATI_DAFSTG uses gradient of the history as of then for detection. For example,
at
the
fiftieth
iteration,
there
are
three
histories
like
Fig.3-1.Like
them,
OpenATI_DAFSTG calculates gradient of them. Next, from the latest point of history,
OpenATI_DAFSTG draws a prediction line with calculated gradient to the line of
hundredth iterations as the time limit. If the point at the intersection of the prediction
line
with
the
line
of
time
limit
is
less
than
the
convergence
criterion,
OpenATI_DAFSTG estimates the iterative solver will converge. On the other hand,
when the intersection point is greater than the criterion, OpenATI_DAFSTG estimates
the solver will not converge.
Fig. 3-1 The idea of this auto-tuning method
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