MODIFICATION OF THE A.N. TIKHONOV''S METHOD FOR SOLVING APPROXIMATE SYSTEMS OF LINEAR ALGEBRAIC EQUATIONS FOR NON-EUCLIDEAN NORMS
The modification of A.N. Tikhonov’s method for solving approximate system of linear algebraic equations with using vector and matrix norms different from Euclidean is proposed in present article. A generalized formulation of the problem is presented and a series of lemmas and theorems are proved, which allow to reduce this problem to a certain type of mathematical programming problem. Four problems of this class, constructed using polyhedral norms, are described. Their reduction to the problems of mathematical programming are presented. Two problems are considered in more detail. Theorems have been proved that substantiate the reducing these problems to a set of linear programming problems. The results of computational experiments are presented.