Abstract
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.
Highlights
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 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 are presented
Summary
В статье представлен новый метод вычисления обобщённых нормальных решений недоопределённых систем линейных алгебраических уравнений на основе специальных расширенных систем. В статье предлагается новый метод нахождения обобщённых нормальных решений недоопределённых, возможно разреженных и плохо обусловленных, СЛАУ большой размерности на основе специальной расширенной системы. В данной работе для решения задачи (2) предлагается подход, основанный на использовании специальной расширенной системы. Что матрица B при всех > 0 невырожденная и, следовательно, система (12) всегда имеет единственное решение.
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