Smoothing and Regularization with Modified Sparse Approximate Inverses

Figure 3

Reconstruction error against the iteration for the 1D operator 𝐻⁸¹ and original data 𝑥₁ of size 𝑛=10³ affected by random noise of order 0.01%. CG is compared to PCG using the optimal preconditioner 𝑀3_𝜌 (43) for different weights 𝜌.