iiD Seminar: Fast Matrix Multiplication That Does Not Slow Down
In the world of Pokémon, trainers often rely on their trusty Pokémon to battle against other trainers and their Pokémon. However, when a trainer wants to defeat a particularly powerful opponent, they may need to combine the strengths of multiple Pokémon to overcome their enemy. This is similar to how distributed matrix multiplication (DMM) works. In DMM, multiple machines work together to quickly calculate the product of two matrices. But just like a Pokémon trainer, it's important to have a backup plan in case one of the machines fails or loses connection. That's why we propose a hybrid algorithm that combines DMM with fast matrix multiplication (FMM). This combination allows us to take the best of both worlds, providing both speed and reliability. By analyzing the tensor product code structure of the hybrid algorithm, we can prove that it has a positive error exponent, meaning it can withstand errors and continue to function effectively. So just like a trainer would carefully select the right Pokémon for the job, we've chosen the perfect combination of DMM and FMM to quickly and reliably calculate matrix products.