Algorithm 2: Adaptive Kaczmarz method

Input: orthonormal current matrix T, initial conductivity guess ρ(0), number of iterations m

Initialize T̂ = T, ρ = ρ(0);

for k =1:mdo

a. repeat

Apply T̂ and measure voltages V; Apply T̂ and compute the simulated voltages U(ρ); Form the voltage difference matrix D = V − U(ρ) and P = D*D; Perform eigenvalue decomposition of P and form the eigenvector matrix E so that their corresponding eigenvalues are sorted in descending order; T̂ = T̂E; until

the current pattern converges;

b. Obtained the ordered subsets $I=\{I_{\mathit{\text{sub}}}^1,I_{\mathit{\text{sub}}}^2,\dots ,I_{\mathit{\text{sub}}}^n\}$, $$V=\{V_{\mathit{\text{sub}}}^1,V_{\mathit{\text{sub}}}^2,\dots ,V_{\mathit{\text{sub}}}^n\}$$, the row submatrix J = {J1, J2, …, Jn}, ρ0 = ρ;

c. for i=1:ndo $${\rho }_i={\rho }_{i-1}+a_i{J}_i^T{(J_{k,i}{J}_i^T+{\lambda }_{i}I)}^{-1}(V_i-U_i({\rho }_{i-1}));$$

end

d. ρ = ρn;

end

Output: conductivity distribution ρ