Application of the concept of the conditioning of a matrix to an identification problem

AbstractIn the solution of a linear system of equations, the initial errors in the coefficients (e.g. due to experimental errors) and the errors of calculation involved in the solution (e.g. rounding errors) have a varying effect on the accuracy of the solution obtained. The concept of the conditioning of a matrix makes it possible to measure the extent to which a linear system is capable of being accurately solved. Here we consider the application of this idea to a study of the influence of errors in an identification problem. The experimental conditions are sought which will allow the most accurate possible identification of the unknown parameters from the results of the corresponding experiment