Fast hybrid matrix multiplication algorithms

New hybrid algorithms for matrix multiplication are proposed that have the lowest computational complexity in comparison with well-known matrix multiplication algorithms. Based on the proposed algorithms, efficient algorithms are developed for the basic operation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ D = C + \sum\limits_{l =1}^{\xi} A_{l} B_{l}$\end{document} of cellular methods of linear algebra, where A, B, and D are square matrices of cell size. The computational complexity of the proposed algorithms is estimated.