People tend to obsess over making computer software faster. You can, of course, just crank up the clock speed and add more processors, but often the most powerful way to make something faster is to ...

Improving the efficiency of algorithms for fundamental computations can have a widespread impact, as it can affect the overall speed of a large amount of computations. Matrix multiplication is one ...

Matrix multiplication runs the modern world. For every word that ChatGPT writes, I estimate that ~10,000,000,000 (10 billion) small matrices must be multiplied. Modern gaming engines routinely draw 10 ...

With AlphaTensor, DeepMind Technologies has presented an AI system that is supposed to independently find novel, efficient and provably correct algorithms for complex mathematical tasks. AlphaTensor ...

This is an implementation of the Karatsuba polynomial multiplication algorithm in the LEGv8 assembly language, a RISC ISA part of the ARM architecture family. This was done as my final project for ECE ...

This project implements matrix multiplication optimization using Strassen's algorithm, a divide-and-conquer approach that reduces the complexity of matrix multiplication from (O(n^3)) to approximately ...

Mathematicians love a good puzzle. Even something as abstract as multiplying matrices (two-dimensional tables of numbers) can feel like a game when you try to find the most efficient way to do it.

Abstract: Large-integer modular multiplication (LMM) is a core operation in public-key algorithms, which serve as critical safeguards for information security. Although much effort has been made to ...

Progressive formalization is the gradual movement from informal problem-solving toward formal mathematical reasoning. Rather than starting with abstract algorithms, it builds from students’ intuitive ...