  We present a computable reformulation of Ruelle's linear response formula for
chaotic systems. The new formula, called Space-Split Sensitivity or S3,
achieves an error convergence of the order ${\cal O}(1/\sqrt{N})$ using $N$
phase points. The reformulation is based on splitting the overall sensitivity
into that to stable and unstable components of the perturbation. The unstable
contribution to the sensitivity is regularized using ergodic properties and the
hyperbolic structure of the dynamics. Numerical examples of uniformly
hyperbolic attractors are used to validate the S3 formula against a na\"ive
finite-difference calculation; sensitivities match closely, with far fewer
sample points required by S3.
