The concept of Short Recycling was first presented on 24th of November 2015 at TU Delft with the following slides:
Presentation .
![Convergence example](SR_Example_Poisson.PNG)
Figure 1: Exemplary convergence curves for SRIDR(10) and SRBiCG on
a 100x100 finte difference discretisation of a Poisson problem.
Fig. 1 shows the convergence behaviour
SRIDR(10) and SRBiCG for a Poisson problem. One can observe that
the recycling methods yield a faster convergence than their
predecessors IDR(10) and BiCG. The overhead due to the recycling is 6
extra DOT products for SRBiCG compared to BiCG per matrix-vector
product (#MV) during the first 40 iterations and an additional storage
for 40 column vectors of length 10000. For SRIDR(10) there is no
overhead at all, neither in computations nor in storage.
![Numerical experiments for Mstab.](Mstab_convdiffreac.png)
Figure 2: Redundant solution of central FD discretised PDEs. We observe that Mstab converges earlier than IDRstab.
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![](Mstab_sequences.png)
Figure 3: Further test cases.
![](Mstab_some_testcases.png)
Figure 4: Comparative study of IDRstab vs. Mstab on a parametric test case.
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![Experimental verification of the termination behaviour of Mstab and IDRstab.](Mstab_small_termination.png)
Figure 5: Comparison of the termination behaviour of IDRstab and Mstab.
The spaces G and M are the last spaces before the respective methods terminate.