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Table 2 Times spend in different subtasks in the RADI iteration and RKSM for CUBE with \(m=p=10\)

From: RADI: a low-rank ADI-type algorithm for large scale algebraic Riccati equations

Method Subtask Time
RADI—Penzl: 135 iterations Precompute shifts 5.31
Solve linear systems 43.24
Total 49.19
RADI—Ham, \(\ell =2p\): 139 iterations Solve linear systems 46.42
Compute shifts dynamically 1.76
Total 48.79
RADI—Ham, \(\ell =6p\): 100 iterations Solve linear systems 32.73
Compute shifts dynamically 2.75
Total 35.92
RADI—Ham, \(\ell =\infty \): 74 iterations Solve linear systems 24.74
Compute shifts dynamically 32.44
Total 57.51
RKSM—adaptive: 79 iterations Solve linear systems 18.45
Orthogonalization 4.14
Compute shifts dynamically 12.02
Solve projected equations 15.98
Total 53.82