This Pixar Animation Studios Technical Report by Kass, Lefohn, and Owens describes a GPU-based data-parallel direct tridiagonal linear solver. To the authors’ knowledge, this is the first reported direct, linear-time tridiagonal GPU solver. The solver is used to implement a new heat-diffusion-based depth-of-field preview algorithm; and the paper describes solving thousands of tridiagonal systems, each with hundreds of elements, on the GPU at interactive rendering rates. The alternating direction implicit solution gives rise to separable spatially varying recursive (infinite-impulse response, IIR) filters that can compute large-kernel convolutions in constant time per pixel while respecting the boundaries between in-focus and out-of-focus objects. Recursive filters have traditionally been viewed as problematic for GPUs, but using the well-established method of cyclic reduction of tridiagonal systems, the authors are able to parallelize the computation and implement an efficient solution in terms of GPGPU primitives. (Michael Kass, Aaron Lefohn, and John Owens. Interactive Depth of Field Using Simulated Diffusion on the GPU, Technical Report #06-01, Pixar Animation Studios, January 2006.)