Jean-Guillaume Dumas

Title: Jean-Guillaume Dumas

Main Research Question: How can we efficiently compute the dot product of two vectors over word-size finite fields?

Methodology: The study compares the practical behaviors of a wide range of implementation techniques using different representations. These techniques include floating point representations, discrete logarithms, tabulations, Montgomery reduction, and delayed modulus.

Results: The research found that Montgomery representation is a promising approach for achieving efficiency in the computation of the dot product. It allows for significant reduction in the cost of machine remainders, making it a viable alternative to classical representations.

Implications: The study's findings have important implications for the field of linear algebra and matrix manipulations. The efficient computation of the dot product over finite fields can lead to faster algorithms for matrix multiplication, triangular system solving, and matrix factorizations. Additionally, the research contributes to the ongoing development of efficient algorithms for iterative methods, further advancing the state of the art in numerical analysis.

Link to Article: https://arxiv.org/abs/0404008v2 Authors: arXiv ID: 0404008v2