AIR Tools - A MATLAB Package for Algebraic Iterative ...

List of Figures
2.1 SVD basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Picard plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Illustration of basis semi-convergence . . . . . . . . . . . . . . . . 10
3.1 Cimmino’s reflection method . . . . . . . . . . . . . . . . . . . . 16
3.2 Cimmino’s projection method . . . . . . . . . . . . . . . . . . . . 18
3.3 Kaczmarz’s method . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.4 Symmetric Kaczmarz . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.1 Behaviour of Φ k (σ, λ) and Ψ k (σ, λ). . . . . . . . . . . . . . . . . 37
4.2 Ψ k (σ, λ) as function of σ . . . . . . . . . . . . . . . . . . . . . . . 39
4.3 Relative error histories for nine values of λ . . . . . . . . . . . . . 40
4.4 The minimum relative errors for different λ-values . . . . . . . . 40
4.5 Optimal number of iterations for a SIRT method . . . . . . . . . 41