  A sketch-and-select Arnoldi process to generate a well-conditioned basis of a
Krylov space at low cost is proposed. At each iteration the procedure utilizes
randomized sketching to select a limited number of previously computed basis
vectors to project out of the current basis vector. The computational cost
grows linearly with the dimension of the Krylov space. The subset selection
problem for the projection step is approximately solved with a number of
heuristic algorithms and greedy methods used in statistical learning and
compressive sensing.
