Open AccessThe Use of Solvable Directed Graphs in a Jacobi-like Algorithm
Author(s) -
Meltem Sönmez Turan
Publication year - 2021
Publication title -
european journal of mathematics and statistics
Language(s) - English
Resource type - Journals
ISSN - 2736-5484
DOI - 10.24018/ejmath.2021.2.3.39
Subject(s) - sequence (biology) , convergence (economics) , mathematics , algorithm , matrix (chemical analysis) , quadratic equation , similarity (geometry) , triangular matrix , directed graph , combinatorics , discrete mathematics , computer science , pure mathematics , artificial intelligence , genetics , materials science , geometry , image (mathematics) , invertible matrix , economics , composite material , biology , economic growth
In this paper, we introduce a Jacobi-like algorithm (we call D-NJLA) to reduce a real nonsymmetric n × n matrix to a real upper triangular form by the help of solvable directed graphs. This method uses only real arithmetic and a sequence of orthogonal similarity transformations and achieves ultimate quadratic convergence. A theoretical analysis is constructed and some experimental results are given.