A Direct Error Measure for Affine Models of Nonlinear Algebraic Systems
D M. Lorenzetti
This paper proposes a measure of the deviation between a nonlinear equation and its affine model, and demonstrates applications to nonlinear systems. The measure expresses the model error relative to a representative change in its predicted value. Aggregating across a nonlinear system indicates the spatial extent of the system model's predicitive capability, and, unlike a cost function, reflects direction as well as length differences between the predicted and actual residuals. Used to examine the trial points generated by an existing descent method, the new measure identifies other problems inherent in the cost function approach. These observations lead to a modified descent method, whose trust radius responds to the relative error. Numerical tests show these changes improve the solver's performance on a standard suite of nonlinear algebraic systems.
Siam Journal on Scientific Computing
affine model, error measure, Newton-Raphson, nonlinear system, trust region