A geometric property of the functional associated with general systems of algebraic equations
I.R. Ciric · International Symposium on Antenna Technology and Applied Electromagnetics · 2006
A functional is associated to general systems of linear algebraic equations such that, for any point defined by an arbitrary set of unknowns, the position along its gradient which is the nearest to the system solution point can be determined directly from the value of the functional and of the gradient. Remarkably, the distance along the gradient to the point closest to the solution point is equal to the ratio of the value of the functional to the magnitude of its gradient at the starting point. By means of simple matrix transformations, this property can be employed to construct independent equations satisfied only by a part of the original system unknowns.