Study On Preconditioned GAOR Methods For A Class Of 2×2 Block Linear Systems

Solutions of block linear systems arise from mathematics,physics,statistics,the large-scale scientific computing and engineering technique,and social sciences.For example,the classical generalized least squares problem has a wide range of scientific application background in many scientific fields,and the most typical application is parameter estimation in mathematical model.In order to solve the generalized least squares problem,it is generally transformed into a class of block 2 × 2 linear systems to solve it.In this paper,we mainly study the solution of the block 2 × 2 linear systems arising from the generalized least squares problem.The solution of this problem has both important theoretical significance and application value for the solution of the block linear system.In order to accelerate the convergence rate of GAOR method,we give different preconditioners and the corresponding conver-gence theory.Finally,we give numerical experiments to verify the feasibility and effectiveness of the proposed methods.