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inexact_newton


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 -- Command: [X, FVAL, EXITFLAG, OUTPUT, JACOBIAN] = inexact_newton
          (@FUN, X0, [OPTIONS])

     Solve the nonlinear equation ‘f(x) = 0’ using the inexact Newton
     method, starting from the initial guess X0.

     If an exact jacobian is not provided it is approximated by finite
     differences, if the method for solving linear systems is not
     specified it is set as defaults to ’GMRES’, other possible values
     are ’PCG’ or ’BICGSTAB’.

     First output parameter X is the computed solution.

     Second output parameter is @FVAL that is the value of the function
     at computed solution.

     Third output parameter is exitflag and it has not yet been
     implemented.

     Fourth output parameter is output which is a struct containing the
     field ’ITERATIONS’ that is the number if iterations required to
     converge and ’FUNCCOUNT’ which contains the number of function
     evaluations computed.

     Last output argument is jacobian and is the value of the Jacobian
     at the computed solution.

     The first input parameter @FUN must be a function_handle.

     The second input argument X0 must be the initial guess.

     The third input argument is optional and describes a set of options
     useful to adapt the computation to what is needed.  Possible fields
     are
     ‘UseJacobian’
          is a switch variable [’YES’,’NO’] that tells the program how
          to set the ’JACOBIAN’ option within optimset function,
     ‘NewtonTol’
          tolerance for termination test on residual,
     ‘MaxNewtonIterations’
          maximum number of nonlinear iterations,
     ‘Eta’
          initial forcing term (must be in the interval [0,1)).  For
          details see [1],
     ‘Choice’
          formula to use to select the forcing term may be 1 or 2,
          default value is 1.  For details see [1],
     ‘Algorithm’
          iterative method to solve the linearized system (default is
          ‘'GMRES'’),
     ‘Restart’
          restart parameter for the GMRES solver (ignored for other
          solvers).

     References: [1] S.C. Eisenstat and H.F. Walker, "Choosing the
     Forcing Terms in an Inexact Newton Method."  SIAM Journal on
     Scientific Computing, 17(1), pp.  16-16, 1996.

See also: gmres, pcg, bicgstab, odebwe.


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Solve the nonlinear equation ‘f(x) = 0’ using the inexact Newton method,
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