Solving a sparse system using linear algebra. (March 2016)

• Record Type: Journal Article
• Authors: Massri, César
• Is Part Of: Journal of symbolic computation. Volume 73(2016)
• Page Start: 157
• Page End: 174
• Publication Date: 2016-03
• Subjects: 14M25 -- 13P15; Multiplication matrix -- Eigenvector -- Sparse system -- Toric varieties; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2015.06.003
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We give a new theoretical tool to solve sparse systems with finitely many solutions. It is based on toric varieties and basic linear algebra; eigenvalues, eigenvectors and coefficient matrices. We adapt Eigenvalue theorem and Eigenvector theorem to work with a canonical rectangular matrix (the first Koszul map) and prove that these new theorems serve to solve overdetermined sparse systems and to count the expected number of solutions.