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 Saebyuk May 10, 1999 08:25

HI, CFDians !

What is Newton-GMRES ? what is the difference between GMRES and Newton-GMRES ?

 F. Olawsky May 20, 1999 06:13

Hi!

(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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