Algebraic complexity theory deals with the computation of polynomials using the basic operations addition and multiplication. For example, we can compute the polynomial \(xy + xz\) using two ...

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 ...

A paper posted online in March 2019 presents what may be essentially the fastest possible algorithm for one of the oldest problems in mathematics: whole number multiplication. The new algorithm, which ...

Several algorithms based on homogeneous polynomials for multiplication of large integers are described in the paper. The homogeneity of polynomials provides several simplifications: reduction of ...

Abstract: In the sparse polynomial multiplication problem, one is asked to multiply two sparse polynomials f and g in time that is proportional to the size of the input plus the size of the output.

We study real-life problems via mathematical models, which usually tend to be nonlinear systems, or equations. A standard trick is to “linearize” this nonlinear system. The newly obtained system then ...