The motivation for it was provided by Dr. Richard L. Garwin at IBM Watson Research who was concerned about verifying a nuclear arms treaty with the Soviet Union for the SALT talks. Garwin thought that if he had a very much faster Fourier Transform he could plant sensors in the ground in countries surrounding the Soviet Union. He suggested to both Cooley and Tukey how Fourier transforms could be programmed to be much faster. They did the work, the sensors were planted, and he was able to locate nuclear explosions to within 15 kilometers of where they were occurring.
James W. Cooley (1961): "An improved eigenvalue corrector formula for solving the Schrödinger equation for central fields", Math. Comput. 15, 363–374. doi:10.1090/S0025-5718-1961-0129566-X This describes the so-called Numerov-Cooley method for numerically solving one-dimensional Schrödinger equations.
Cooley, James W., Timothy M. Toolan and Donald W. Tufts. "A Subspace Tracking Algorithm Using the Fast Fourier Transform." IEEE Signal Processing Letters. 11(1):30–32. January 2004.
Real, Edward C., Donald W. Tufts and James W. Cooley. "Two Algorithms for Fast Approximate Subspace Tracking." IEEE Transactions on Signal Processing. 47(7):1936–1945. July 1999.
^ abCooley, James. "The Re-Discovery of the Fast Fourier Transform Algorithm"(PDF). web.cs.dal.ca. Archived from the original(PDF) on 2012-12-24. However, we had a previous collaboration in 1953 when Tukey was a consultant at John Von Neuman's computer project at the Institute for Advanced Study in Princeton, New Jersey, where I was a programmer. I programmed for him what later became the very popular Blackman-Tukey method of spectral analysis [5]. The important feature of this method was that it gave good smoothed statistical estimates of power spectra without requiring large Fourier transforms. Thus, our two collaborations were first on a method for avoiding large Fourier transforms since they were so costly and then a method for reducing the cost of the Fourier transforms.
