Solving a sparse system using linear algebra

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...

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Detalles Bibliográficos
Autor principal: Massri, C.
Formato: JOUR
Materias:
Eigenvector
Multiplication matrix
Sparse system
Toric varieties
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_07477171_v73_n_p157_Massri
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_07477171_v73_n_p157_Massri
record_format dspace
spelling todo:paper_07477171_v73_n_p157_Massri2023-10-03T15:39:00Z Solving a sparse system using linear algebra Massri, C. Eigenvector Multiplication matrix Sparse system Toric varieties 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. © 2015 Elsevier Ltd. Fil:Massri, C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_07477171_v73_n_p157_Massri
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Eigenvector
Multiplication matrix
Sparse system
Toric varieties
spellingShingle Eigenvector
Multiplication matrix
Sparse system
Toric varieties
Massri, C.
Solving a sparse system using linear algebra
topic_facet Eigenvector
Multiplication matrix
Sparse system
Toric varieties
description 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. © 2015 Elsevier Ltd.
format JOUR
author Massri, C.
author_facet Massri, C.
author_sort Massri, C.
title Solving a sparse system using linear algebra
title_short Solving a sparse system using linear algebra
title_full Solving a sparse system using linear algebra
title_fullStr Solving a sparse system using linear algebra
title_full_unstemmed Solving a sparse system using linear algebra
title_sort solving a sparse system using linear algebra
url http://hdl.handle.net/20.500.12110/paper_07477171_v73_n_p157_Massri
work_keys_str_mv AT massric solvingasparsesystemusinglinearalgebra
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