|May 20, 1999, 06:13||
Re: about Newton-GMRES
(1) GMRES is a method for solving a linear system. The matrix of this system is only used in matrix-vector products!
(2) The Newton-method is a method for solving a nonlinear system of equations. In each iteration step of the Newton-method you need to solve a linear system. The matrix of the linear system is the Jacobian of the nonlinear equations!
(3) If you use a Newton-method with GMRES (or BiCGStab, TFQMR, QMRCGStab,...) the algorithm can be implemented without forming the Jacobian explicitly. You can approximate the matrix-vector products by finite differences. It's called MATRIX-FREE GMRES. If you can use it in this way, you need less memory!
(4) Have a look at this page (link: 'some recent papers'): http://goldfinger.utias.utoronto.ca/~dwz/ These papers are easy to understand.
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