Kaczmarz and Cimmino methods are used for iterative solving of linear systems of equations:
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Cyclic Kaczmarz iterates through each row.
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Randomized Kaczmarz selects the row randomly by probability proportional to row's (Euclidean) norm.
Let $ A \in \mathbb{R}^{m,n} $ the coefficient matrix and $ b \in \mathbb{R}^m $ the constant vector, $ i = k \space mod \space m, \space k \in \mathopen[ 1, N \mathclose] $ (N = nr of iterations) then $$ x^{k+1} = x^{k} + \frac{b^i-r_i^T x^k}{||r||_2^2}r_i $$
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Cimmino considers all rows at once and next iteration vector represents the average value of all previously computed vectors. $$ x^{k+1} = x^{k} + A^T M (b-Ax^k), \space M = diag(\frac{1}{m||r_i||_2^2}) $$
To run the application you need to have installed the python packages from requirements.txt.
Application starts by running the gui.py script.
