第二讲求根方法.pptVIP

求根方法 工程中的数值方法 问题的提出 医学研究表明,如果在自由下落4s后自由落体速度超过了36m/s，那么蹦极运动员持续大幅度损伤的概率会显著增加。为此，希望确定在给定0.25kg/m的阻尼系数下超越该准则的蹦极运动员的质量是多少？ 是否能将质量m显式表示 使该函数等于0的m值 图形法 cd =.25; g = 9.81; v = 36; t = 4; mp = linspace(50,200); fp = sqrt(g*mp/cd).*tanh(sqrt(g*cd./mp)*t)-v; plot(mp,fp), grid sqrt(g*145/cd)*tanh(sqrt(g*cd/145)*t)-v ans = 0.045626491526377 划界法与初值猜测值 两个初始猜测值基础上，并要求这两个猜测值界定的区间包含根，这两个初始值必须在该根的两边 增量有哪些信誉好的足球投注网站 f(x)是从xl到xu区间上的连续函数，且f(xl)和f(xu)的符号相反，那么xl到xu至少存在一个实根 实现增量有哪些信誉好的足球投注网站的incsearch函数 function xb = incsearch(func,xmin,xmax,ns) % incsearch: incremental search root locator % xb = incsearch(func,xmin,xmax,ns): % finds brackets of x that contain sign changes % of a function on an interval % input: % func = name of function % xmin, xmax = endpoints of interval % ns = number of subintervals (default = 50) % output: % xb(k,1) is the lower bound of the kth sign change % xb(k,2) is the upper bound of the kth sign change % If no brackets found, xb = []. if nargin 4, ns = 50; end %if ns blank set to 50 % Incremental search x = linspace(xmin,xmax,ns); f = func(x); nb = 0; xb = []; %xb is null unless sign change detected for k = 1:length(x)-1 if sign(f(k)) ~= sign(f(k+1)) %check for sign change nb = nb + 1; xb(nb,1) = x(k); xb(nb,2) = x(k+1); end end if isempty(xb) %display that no brackets were found disp(no brackets found) disp(check interval or increase ns) else disp(number of brackets:) %display number of brackets disp(nb) end incsearch(@(x) sin(10*x)+cos(3*x),3,6) number of brackets: 5 ans = 3.244897959183673 3.306122448979592 3.306122448979592 3.367346938775510 3.734693877551020 3.795918367346939 4.653061224489796 4.714285714285714 5.632653061224490 5.693877551020409 y = 3:0.01:6; x = 3:0.01:6; y = sin(10*x)+cos(3*x); grid; plot(x,y) x1 = incsearch(@(x) sin(10*x)+cos(3*x),3,6); hold on; plot(x1(:,1),0,‘*’); hold on; plot(x1(:,2),0,*); grid on; 二分法（Bisection method) 一般地，对于函数f(x),如果存在实数c,当x