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nsoli

nsoli Newton-Krylov solver, globally convergent solver for f(x) = 0. Inexact-Newton-Armijo iteration Eisenstat-Walker forcing term Parabolic line search via three point interpolation. C. T. Kelley, April 27, 2001 This code comes with no guarantee or warranty of any kind. This is a modification by Christophe Gouel of the original file, which can be downloaded from: http://www4.ncsu.edu/~ctk/newtony.html The changes are surrounded above and below by "%% Change CG" % and "%%". They only concern the way of handling inputs (particularly options). INPUT function = f initial iterate = x options = structure whose fields are atol : absolute error tolerances for the nonlinear iteration (default = sqrt(eps)) rtol : absolute error tolerances for the nonlinear iteration (default = sqrt(eps)) maxit : maximum number of nonlinear iterations (default = 40) lmaxit : maximum number of inner iterations before restart. In GMRES(m), m = maxitl. For iterative methods other than GMRES(m) maxitl is the upper bound on linear iterations (default = 40). showiters : display iteration (default = 0) etamax : Maximum error tolerance for residual in inner iteration. The inner iteration terminates when the relative linear residual is smaller than eta*|F(x_c)|. eta is determined by the modified Eisenstat-Walker formula if etamax > 0. If etamax < 0, then eta = |etamax| for the entire iteration. (default = .9) lmeth : choice of linear iterative method 1 (GMRES), 2 GMRES(m), 3 (BICGSTAB), 4 (TFQMR) (default = 1 (GMRES, no restarts)) restart_limit : max number of restarts for GMRES if lmeth = 2 (default = 20) OUTPUT sol = solution it_hist(maxit,3) = l2 norms of nonlinear residuals for the iteration, number of function evaluations, and number of steplength reductions ierr = 0 upon successful termination ierr = 1 if after maxit iterations the termination criterion is not satsified ierr = 2 failure in the line search. The iteration is terminated if too many steplength reductions are taken. x_hist = matrix of the entire interation history. The columns are the nonlinear iterates. This is useful for making movies, for example, but can consume way too much storage. This is an OPTIONAL argument. Storage is only allocated if x_hist is in the output argument list. internal parameters: alpha = 1.d-4, parameter to measure sufficient decrease sigma0 = .1, sigma1 = .5, safeguarding bounds for the linesearch maxarm = 20, maximum number of steplength reductions before failure is reported