9633326 Laub Standard approaches to measuring the condition of various problems in control theory, such as solving an algebraic Riccati equation (ARE), compress all sensitivity information into a single condition number. Thus, a loss of information can occur in situations in which this standard condition number does not accurately reflect the actual sensitivity of a solution or particular entries of a solution. In this project we shall investigate a new method that overcomes these and other common deficiencies. The new procedure measures the effects on the solution of small random changes in the input data and, by properly scaling the results, obtains condition estimates for each entry of a computed solution. This approach, which is referred to as small-sample statistical condition estimation (SCE), applies to both linear and nonlinear problems. In the former case (for example, when solving a system of linear equations or a linear least squares problem), an explicit Frechet derivative of the computed quantity is available. Thus the method is especially efficient and, in fact, costs no more than standard normwise or componentwise estimates. Even in the nonlinear case (for example, solving AREs), considerable efficiencies are gained when iterative improvement by, say, Newton's method is available. SCE also has the advantage of considerable flexibility. For example, it easily accommodates restrictions on, or structure associated with, allowable perturbations. The method has a rigorous statistical theory available for the probability of accuracy of the condition estimates. Finally,it is emphasized that SCE lends itself readily to straightforward implementation into many existing computer- aided control system design software packages. ***
