Algorithm for Constructing a Solution in a Parallelepiped of a System of Linear Equations with a Parameter from a Rectangle
Аннотация
The problem under consideration involves constructing solutions within a parallelepiped for a system of linear equations that depends on a parameter defined within a rectangle. First, it is determined whether the system of linear equations has a solution in the parallelepiped for some value of the parameter within the rectangle. If such a parameter value is found, a linear programming problem is solved for that parameter. Using the basis that identifies this solution, the region of parameter values for which the system of linear equations has solutions in the parallelepiped is determined. The neighboring regions along the boundaries of this region (a polygon) are then identified, where the system also has solutions within the parallelepiped. By repeating this process a finite number of times, the problem under consideration is solved.