Kaczmarz Iterative Projection and Nonuniform Sampling with Complexity Estimates

Algorithm 1

Randomized Kaczmarz (of [4]).

Require: An over-determined linear set of consistent equations , where is matrix and .

 Let be the rows of and be the th element of .

 (1) Pick an arbitrary initial approximation .

 (2) Set .

 (3) while not converged do

 (4)   Randomly choose from with probability proportional to .

 (5)   

 (6)   Set

 (7) end while