Several Randomized Algorithms For Solving Indefinite Least Squares Problems

As an extension of the linear least squares problem,the indefinite least squares problem has been widely used in many fields,such as the total least squares problem,finite memory adaptive filtering,Errors in Variable(EIV)model,etc.Therefore,it is of extensive significance to study the solution of the indefinite least squares problem.The randomized algorithm for solving the linear least squares problem was first proposed by Strohmer & verhynin [40],and then a series of variants of this algorithm were put forward one after another.On the basis of solving the linear least squares problems with randomized algorithm,this paper puts forward a variant,that is,solving the indefinite least squares problem with randomized algorithm.We propose a randomized Gauss-Seidel algorithm for solving the indefinite least squares problem,a new randomized Gauss-Seidel algorithm and a maximum residual block Gauss-Seidel algorithm for solving the indefinite least squares problem by analogy.Three randomized algorithms and their convergence are analyzed respectively.Numerical experiments show the feasibility and effectiveness of the three algorithms,and the computing time of the new randomized Gauss-Seidel algorithm are better than the maximum residual block Gauss-Seidel algorithm,the maximum residual block Gauss-Seidel algorithm are better than the randomized Gauss-Seidel algorithm,and the new randomized Gauss-Seidel algorithm is superior to the randomized Gauss-Seidel algorithm in iteration times.