by Dan Feng, Thomas H. Pulliam
http://www.nas.nasa.gov/~pulliam/./research_interest/../mypapers/Tensor_GMRES.ps
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Abstract:
This paper introduces a tensor-Krylov method, the tensor-GMRES method, for large sparse systems of nonlinear equations. This method is a coupling of tensor model formation and solution techniques for nonlinear equations with Krylov subspace projection techniques for unsymmetric systems of linear equations. An extension of a NewtonGMRES scheme is used to avoid the factorization of the Jacobian matrix required by traditional tensor methods in forming and solving the tensor model. Like traditional tensor methods, we show that the new tensor method has significant computational advantages over the analogous Newton counterpart on both nonsingular and singular problems. For example, test results on an application to the Euler equations for flow through a nozzle with a given area ratio show that the tensor-GMRES method is 6 times as efficient as an analogous Newton-GMRES method. The new tensor method is also consistent with preconditioning and matrix free implementation.
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