Perturbation Analysis And Condition Numbers Of Scaled Total Least Squares Problems And Symmetric Algebraic Riccati Equations

In this paper,we first give explicit expressions for the estimates of the normwise, mixed and componentwise condition numbers for the scaled total least squares(STLS) problem.Since the total least squares(TLS) problem is a special case of the STLS problem,the condition numbers for the TLS problem follow immediately from our STLS results.All the discussions in this paper are under the Golub-Van Loan condition for the existence and uniqueness of the STLS solution.Numerical experiments show that our results are effective.The second part of this paper is devoted to the perturbation analysis of symmetric algebraic Riccati equations.Based on our perturbation analysis, the upper bounds for the normwise,mixed and componentwise condition numbers are presented.The results are demonstrated by our preliminary numerical examples.