This is a high level post about algorithms (especially mathematical, scientific, and data analysis algorithms) which I hope can help people who are not researchers or numerical software developers better understand how to choose and evaluate algorithms. When scientists and programmers think about efficiency of algorithms, they tend to think about high level ideas like temporary arrays, choice of language, and parallelism. Or they tend to think about low level ideas like pointer indirection, cache efficiency, and SIMD vectorization. However, while these features matter, most decent implementations of the same algorithm tend to get quite close in efficiency to each other (probably <3x if everyone is using a performant enough programming language or constructs). If you're sitting down thinking "what is the next algorithm that I am going to invent that will be truly a step beyond what existed before?", ... READ MORE

I am pleased to announce the release of DifferentialEquations.jl 3.0. In the last DiffEq blog post I described the current state of JuliaDiffEq and DifferentialEquations.jl along with the trajectory that we hoped to take. We identified (at that time) current shortcomings of the software and our plans to remedy them. I also recently did a survey of differential equation suites in order to understand where we stand and see where we need to improve. These research efforts were used to put together a list of goals that were systematically achieved during 3.0. What I would like to do this time around is give a broad overview of what we have released in the 3.0 timeframe, the goals that we have achieved, and the goals that we are putting off (for next Google Summer of Code?). And then, … READ MORE