Open AccessOn a method for calculating generalized normal solutions of underdetermined linear systems
Author(s) -
А. И. Жданов,
Yu. V. Sidorov
Publication year - 2020
Publication title -
kompʹûternaâ optika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 29
eISSN - 2412-6179
pISSN - 0134-2452
DOI - 10.18287/2412-6179-co-607
Subject(s) - underdetermined system , generalized minimal residual method , dimension (graph theory) , mathematics , linear system , system of linear equations , residual , iterative method , computer science , algebraic number , algebraic equation , linear equation , mathematical optimization , algorithm , nonlinear system , mathematical analysis , pure mathematics , physics , quantum mechanics
The article presents a novel algorithm for calculating generalized normal solutions of underdetermined systems of linear algebraic equations based on special extended systems. The advantage of this method is the ability to solve very poorly conditioned (possibly sparse) underdetermined linear systems of large dimension using modern versions of the iterative refinement method based on the generalized minimum residual method (GMRES - IT). Results of applying the considered algorithm to solve the problem of balancing chemical equations (mass balance) are presented.