MATLAB牛顿法源代码.docVIP

MATLAB牛顿法源代码 function [sol, it_hist, ierr] = nsol(x,f,tol,parms)% Newton solver, locally convergent % solver for f(x) = 0%% Hybrid of Newton, Shamanskii, Chord%% C. T. Kelley, November 26, 1993%% This code comes with no guarantee or warranty of any kind.%% function [sol, it_hist, ierr] = nsol(x,f,tol,parms)%% inputs:%??????? initial iterate = x%?? function = f%??????? tol = [atol, rtol] relative/absolute%??? error tolerances% parms = [maxit, isham, rsham]%??? maxit = maxmium number of iterations%???? default = 40%?? isham, rsham: The Jacobian matrix is% ?? computed and factored after isham%?????????????? updates of x or whenever the ratio%?? of successive infinity norms of the%?????????????? nonlinear residual exceeds rsham.%??? isham = 1, rsham = 0 is Newtons method,%??? isham = -1, rsham = 1 is the chord method,% ??? isham = m, rsham = 1 is the Shamanskii method%????? ??????? defaults = [40, 1000, .5]%% output:% sol = solution% it_hist = infinity norms of nonlinear residuals%??? for the iteration% ierr = 0 upon successful termination% ierr = 1 if either after maxit iterations%???????????? the termination criterion is not satsified%???????????? or the ratio of successive nonlinear residuals%???????????? exceeds 1. In this latter case, the iteration%???? is terminted.%%% internal parameter:%?????? debug = turns on/off iteration statistics display as%?????????????? the iteration progresses%% Requires: diffjac.m, dirder.m%% Here is an example. The example computes pi as a root of sin(x)% with Newtons method and plots the iteration history.%%% x=3; tol=[1.d-6, 1.d-6]; params=[40, 1, 0];% [result, errs, it_hist] = nsol(x, sin, tol, params);% result% semilogy(errs)% %% set the debug parameter, 1 turns display on, otherwise off%debug=0;%% initialize it_hist, ierr, and set the iteration parameters%ierr = 0;maxit=40;isham=1000;rsham=.5;if nargin == 4maxit=parms(1); isham=parms(2); rsham=parms(3);endrtol=t