AbstractA data compression method is presented that is generally applicable to first‐order convergent iterative procedures that employ subspace expansions or extrapolations based on successive correction vectors. This method is based on the truncation of insignificant information in successive correction vectors. Although the correction vectors themselves may be severely truncated with the proposed approach, the final solution vector may be represented to arbitrary accuracy. A feature of the proposed method is that more slowly convergent iterative procedures allow the correction vectors to be more severely truncated without affecting the overall convergence rate. The method is implemented and applied to the iterative Davidson diagonalization method. If the compressed representation of the expansion vectors can be held in main computer memory, then a significant reduction in the I/O requirements is achieve