The simplified version of the Spielman and Srivastava algorithm for   proving the Bourgain-Tzafriri restricted invertiblity theorem
  By giving up the best constants, we will see that the original argument of Spielman and Srivastava for proving the Bourgain-Tzafriri Restricted Invertibility Theorem \cite{SS} still works - and is much simplier than the final version. We do not intend on publishing this since it is their argument with just a trivial modification, but we want to make it available to the mathematics community since several people have requested it already. 
Peter G. Casazza
math.FA