Interpretation and Practical Use of Error Propagation Matrices

Abstract

Di#erent kinds of linear systems of equations, Ax = b where A , often occur when solving real-world problems. The singular value decomposition of A can then be used to construct error propagation matrices and by use of these it is possible to investigate how changes in both the matrix A and vector b a#ect the solution x. Theoretical error bounds based on condition numbers indicate the worst case but the use of experimental error analysis makes it possible to also have information about the e#ect of a more limited amount of perturbations and are in that sense more realistic. In this paper it is shown how the e#ect of perturbations can be analyzed by a semiexperimental analysis for the case m = n and m > n. The analysis combines the theory of the error propagation matrices with an experimental error analysis based on randomly generated perturbations that takes the structure of A into account. Keywords : pseudoinverse solution, perturbation theory, singular value decomposition, experimental error analysis Paper III Contents