I attended my first GDC in 2016 and gave a talk on Fixed Point Iteration (FPI)! The video is available here for those with vault creds: http://www.gdcvault.com/play/1023320/Fixed-Point-Iteration-A-Simple . I have also attached a pre-print version of the slides, which has slide notes: FPI_GDC2016_preprint .
Going forwards I will add additional thoughts and notes and further reading links to this page.
Examples / diagram shaders
Shader with just a gerstner wave framed: MstSRN
My general graphing shader (includes gerstner solve): Msl3Ws
Raymarch overview diagram from slide 39: 4sdSR8
Raymarch render diagram with Secant Step alternating on and off, from slide 57: Mdj3W3
‘Milky’ shader (header image) which uses the Secant Step for fast and accurate convergence, from slide 64: Msy3D1
The biggest omission from this talk (due to time constraints) was a discussion of the behaviour in the presence of multiple solutions. Intuitively, the iteration converges to the ‘closest’ solution. We published a paper  that describes and illustrates this, and also provides a technique to catch all possible solutions. We used this to do reprojection of images, spatially to do a stereoscopic post-conversion and temporally to do a 30-60Hz upsampler.
 Bowles, H. and Zimmermann, D. Oceans on a Shoestring: Shape Representation, Meshing and Shading, Advances in Real-Time Rendering in Games course, SIGGRAPH 2013. Project page here.
 Gonzales-Ochoa, C. Water Technology of Uncharted, GDC 2012
 Bowles, H., Mitchell, K., Sumner, B., Moore, J. and Gross, M.. Iterative Image Warping, Eurographics 2012. Project page here.
 Torres, G. and Ricour, H. Technical Challenges of Assassin’s Creed III: Real-Time Water Simulation and High-Quality Linear Gameplay Sequences, SIGGRAPH Asia 2012
 Keinert, B., Schaefer, H., Korndoerfer, J., Ganse, U. and Stamminger, M., Enhanced Sphere Tracing, STAG 2014
 Tessendorf, J. Simulating Ocean Water, SIGGRAPH 2001