Smoothing and Regularization with Modified Sparse Approximate Inverses

Table 4

Optimal reconstruction error ‖𝑥₂−𝑥̃₂‖₂ for the 1D blur operator 𝐻⁴¹ and the original data 𝑥₂. The problem has size 𝑛=10³ and is affected by random noise of order 0.1%. 𝜌=10².

Regularization method		Optimal value	Reached at iter.
Tikhonov (𝛾=0.3)		0.1286	—
CG(𝐻^41)		0.1240	8
PCG(𝐻^41) 𝜌𝑅3𝐺1	no boundary correction	0.1210	130
	𝜏=0.25	0.0433	58
	𝜏=0.25, middle correction	0.0263	52