K.R. Aida-zade
On solving large-scale systems of linear equations with a small number of nonlinear terms
A solution to a system of finite-dimensional equations with the following features is investigated: 1) the system has a high dimensionality; 2) most of the unknowns are linear in the equations; 3) in the equations there is a small number of nonlinear terms depending on a small number of variables. To solve such systems, which are called almost linear in the paper, an approach is proposed, which comes down to first solving two linear systems, and then the nonlinear system. The dimension of the nonlinear system matches the number of variables participating in the original system in a nonlinear form. The solution of an illustrative problem is given.
Keywords: Nonlinear system, Almost linear system, System solution representation, Uniqueness of the solution
On solving large-scale systems of linear equations with a small number of nonlinear terms
A solution to a system of finite-dimensional equations with the following features is investigated: 1) the system has a high dimensionality; 2) most of the unknowns are linear in the equations; 3) in the equations there is a small number of nonlinear terms depending on a small number of variables. To solve such systems, which are called almost linear in the paper, an approach is proposed, which comes down to first solving two linear systems, and then the nonlinear system. The dimension of the nonlinear system matches the number of variables participating in the original system in a nonlinear form. The solution of an illustrative problem is given.
Keywords: Nonlinear system, Almost linear system, System solution representation, Uniqueness of the solution