The Solution of Row-Finite Linear Systems with the Infinite Gauss-Jordan Elimination The Case of Linear Difference Equations with Variable Coefficients

2014/03/11 by Alexandros Paraskevopoulos, Alexandros G. Paraskevopoulos, Paraskevopoulos, Alexandros G.
Computer Science · Mathematics · #15A21 #16S50 #65F05 #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms #Polynomial and algebraic computation #math.FA #msc:15A21 #msc:16S50 #msc:65F05

paper · pdf · doi:10.48550/arxiv.1403.2624

29 pages

arxiv created 2014/03/11 · openalex publication_date 2014/03/11 · arxiv updated 2014/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The construction of the general solution sequence of row-finite linear systems is accomplished by implementing -ad infinitum- the Gauss-Jordan algorithm under a rightmost pivot elimination strategy. The algorithm generates a basis (finite or Schauder) of the homogeneous solution space for row-finite systems. The infinite Gaussian elimination part of the algorithm solves linear difference equations with variable coefficients of regular order, including equations of constant order and of ascending order. The general solution thus obtained can be expressed as a single Hessenbergian.

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