Smoothing and Regularization with Modified Sparse Approximate Inverses

Table 3

Optimal reconstruction error ‖𝑥₁−𝑥̃₁‖₂ for the 1D operator 𝐻⁸¹ and original data 𝑥₁ of size 𝑛=10³ affected by random noise of order 0.01%.

Regularization method		Optimal value	Reached at iteration
CG(𝐻^81)		2.1870⋅10^−4	5
CG(𝐻^81𝑇𝐻^81)		1.8998⋅10^−4	62
PCG(𝐻^81) with 𝑀3𝜌	𝜌=0.4	2.3699⋅10^−4	4
	𝜌=1	1.9746⋅10^−4	12
	𝜌=5	1.9236⋅10^−4	34
	𝜌=10^2	1.9226⋅10^−4	48