Kaczmarz Iterative Projection and Nonuniform Sampling with Complexity Estimates

Algorithm 2

Randomized Kaczmarz Hyperplane Angles.

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)  Randomly choose from with a uniform distribution.

(4)  while not converged do

(5)  Randomly choose from with probability proportional to

(6)  Compute

(7)  Compute

(8)  Set

(9)  Set

(10) end while