Fast multiplication, determinants, and inverses of arrowhead and diagonal-plus-rank-one matrices over associative fields

Autor:	Stor, Nevena Jakovcevic, Slapnicar, Ivan
Rok vydání:	2022
Předmět:	Mathematics - Numerical Analysis 15B99 65F99 15-04
Druh dokumentu:	Working Paper
Popis:	The article considers arrowhead and diagonal-plus-rank-one matrices in F^(nxn) where F in R,C or H. H is a non-commutative field of quaternions. We give unified formulas for fast matrix-vector multiplications, determinants, and inverses for considered matrices. The formulas are unified in the sense that the same formula holds in both, commutative and noncommutative algebras. Each formula requires O(n) arithmetic operations. Most of the formulas hold for block matrices, as well.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2212.10966 Zobrazit plný text záznamu View this record from Arxiv