Tensor-Krylov methods for large nonlinear equations
The author presents results on using iterative methods for the solution of the linear system which arises when using tensor methods for the solution of nonlinear equations. Tensor methods, originally proposed by \textit{R. B. Schnabel} and \textit{P. D. Frank} [SIAM J. Numer. Anal. 21, 815-843 (1984; Zbl 0562.65029)] are preferred to Newton methods when the Jacobian is ill-conditioned or singular at or near the solution. The author focuses on large systems with sparse Jacobian and reports numerical results on a number of difficult test problems which indicate that tensor methods are superior to Newton methods (both using Krylov-subspace-type iterative solvers for the linear equations) in most cases.
scientific article; zbMATH DE number 894725
scientific article