The Karatsuba algorithm is a fast multiplication algorithm published by Anatoly Karatsuba in 1962.
- It is a divide-and-conquer algorithm that reduces the multiplication of two
$$n$$ -digit numbers to three multiplications of$$n/2$$ -digit numbers. - By recursively applying this method, the total number of single-digit multiplications is reduced to
$$n^{\log_2{3}} \approx n^{1.58}$$ . - It is asymptotically faster than the traditional long multiplication algorithm, which requires
$$n^2$$ single-digit multiplications.
This efficiency makes it a significant improvement over conventional multiplication techniques.