Article ID: | iaor19951854 |
Country: | Netherlands |
Volume: | 62 |
Issue: | 2 |
Start Page Number: | 427 |
End Page Number: | 459 |
Publication Date: | Nov 1993 |
Journal: | Mathematical Programming |
Authors: | Schnabel Robert B., Feng Dan, Frank Paul D. |
Tensor methods for nonlinear equations base each iteration upon a standard linear model, augmented by a low rank quadratic term that is selected in such a way that the mode is efficient to form, store, and solve. These methods have been shown to be very efficient and robust computationally, especially on problems where the Jacobian matrix at the root has a small rank deficiency. This paper analyzes the local convergence properties of two versions of tensor methods, on problems where the Jacobian matrix at the root has a null space of rank one. Both methods augment the standard linear model by a rank one quadratic term. The authors show under mild conditions that the sequence of iterates generated by the tensor method based upon an ‘ideal’ tensor model converges locally and two-step Q-superlinearly to the solution with Q-order