To help you understand the algorithm, the video shows a simple two-digit by two-digit multiplication. You can see that the first and last digits are essentially the result of one multiplication.

Karatsuba’s divide-and-conquer multiplication algorithm takes advantage of this saving. Consider a multiplication algorithm that parallels the way multiplication of complex numbers works.

But Anatoly Karatsuba defied the odds, providing a breakthrough with what would come to be known as Karatsuba's Algorithm,a faster, more efficient way to multiply large numbers that would ...

What do encrypted messages, recognizing speech commands and running simulations to predict the weather have in common? They all rely on matrix multiplication for accurate calculations. DeepMind, an ...

High-performance matrix multiplication remains a cornerstone of numerical computing, underpinning a wide array of applications from scientific simulations to machine learning. Researchers ...

According to the mathematicians, from Australia and France, long multiplication used to be the only way to multiply - but proved tedious and time-consuming when the numbers became too large.

By transforming operands into a Montgomery domain, these algorithms enable efficient modular multiplication and exponentiation, which are crucial for public-key cryptosystems.

See all Abstractions blog Even more important, the multiplication algorithm is part of a class of nearly ubiquitous algorithms in computer science. Gidney expects that his new technique will allow ...