实验22用两分法求方程的根 如下的程序是用两分法计算方程在区间[ab]中的根 1)mosa,=|i←0 while b-al 210 a+b c← ←a A:←-b-a a←ciff(a)f(c)>0 b←ciff(c)f(b)>0 1←1+1 f(x):=2x+3.5·x+1.9x-2.5 0 0.75 0.625 0.125 roots(0, 1, f=4 0.5625 0.53125 0.0625 50.53125 0.5625 546 0.03125 6054687505625055468750015625 70.5546875 056250.558593800078125 80.554687505859380.556 0.0039063 90.55664060.55859380.557617200019531 root(f(x),x)=0.558333085242691 f(0.558333085242691)=1.314×10
实验22 用两分法求方程的根 如下的程序是用两分法计算方程在区间[a,b]中的根： (1) roots(a,b,f) i ¬ 0 c a + b 2 ¬ Ai, 0 ¬ a A i, 1 ¬ b A i, 2 ¬ c A i, 3 ¬ b - a a ¬ c if f(a)×f(c) > 0 b ¬ c if f(c)×f(b) > 0 i ¬ i + 1 b - a 10- 3 while ³ A := f(x) 2x 3 3.5 x 2 := + × + 1.9×x - 2.5 roots(0, 1,f) 0 1 2 3 0 1 2 3 4 5 6 7 8 9 0 1 0.5 1 0.5 1 0.75 0.5 0.5 0.75 0.625 0.25 0.5 0.625 0.5625 0.125 0.5 0.5625 0.53125 0.0625 0.53125 0.5625 0.546875 0.03125 0.546875 0.5625 0.5546875 0.015625 0.5546875 0.5625 0.5585938 0.0078125 0.5546875 0.5585938 0.5566406 0.0039063 0.5566406 0.5585938 0.5576172 0.0019531 = 2 0 2 5 5 f(x) x x := 0.8 root(f(x), x) = 0.558333085242691 f(0.558333085242691) 1.314 10- 5 = ´
g(t) 5.1t+75·t-2.9 g(t) 105 2050750625025 30.50.62505630.1 roos(0,1,g)=40.563|06250.594063 505940625 60.594060906020016 9060706090608000 125 32750. 2151751625025 32875025 316251.751 B3|275|2875|2813 roos(1,2,g)=41.6881751719063 roots(2, 3, g) 275281327810.063 517191751.7340031 2.7527812.7660031 617191.73417270016 62766278127730.016 1.719172717230008 2.76627732.770008 817191.72317210004 8277|2.773|2.7710.004 9|1.7191.7211.7200021 2772.7712.771000 f(t):1.3·t-26.013·t-+0.975t-19.50975 f(t)
g(t) t 3 5.1 t 2 := - × + 7.5×t - 2.9 0 5 10 10 g(t) t roots(0, 1,g) 0 1 2 3 0 1 2 3 4 5 6 7 8 9 0 1 0.5 1 0.5 1 0.75 0.5 0.5 0.75 0.625 0.25 0.5 0.625 0.563 0.125 0.563 0.625 0.594 0.063 0.594 0.625 0.609 0.031 0.594 0.609 0.602 0.016 0.602 0.609 0.605 0.008 0.605 0.609 0.607 0.004 0.607 0.609 0.608 0.002 = roots(1, 2,g) 0 1 2 3 0 1 2 3 4 5 6 7 8 9 1 2 1.5 1 1.5 2 1.75 0.5 1.5 1.75 1.625 0.25 1.625 1.75 1.688 0.125 1.688 1.75 1.719 0.063 1.719 1.75 1.734 0.031 1.719 1.734 1.727 0.016 1.719 1.727 1.723 0.008 1.719 1.723 1.721 0.004 1.719 1.721 1.72 0.002 = roots(2, 3,g) 0 1 2 3 0 1 2 3 4 5 6 7 8 9 2 3 2.5 1 2.5 3 2.75 0.5 2.75 3 2.875 0.25 2.75 2.875 2.813 0.125 2.75 2.813 2.781 0.063 2.75 2.781 2.766 0.031 2.766 2.781 2.773 0.016 2.766 2.773 2.77 0.008 2.77 2.773 2.771 0.004 2.77 2.771 2.771 0.002 = f(t) 1.3 t 3 × 26.013 t 2 := - × + 0.975×t - 19.50975 10 0 10 20 2000 f(t) t
0202120.5 20 250.5 220202520.1250.25 roots(20,21,f)= 2020063200310.063 2020.03120 6202001620.00800 72000820016200120008 820.0082001220.010004 2001200122001110002 (2)Bifid(a, b, f ): while (|> 10-5 a +b fag←1 f(a)f(c)>0 while flag ag←0 f(x):=2x+3.5x-+1.9x-2.5 Bifido0,1,f)=0.5583267 root(f(x),x)=0.55833309
roots(20,21,f) 0 1 2 3 0 1 2 3 4 5 6 7 8 9 20 21 20.5 1 20 20.5 20.25 0.5 20 20.25 20.125 0.25 20 20.125 20.063 0.125 20 20.063 20.031 0.063 20 20.031 20.016 0.031 20 20.016 20.008 0.016 20.008 20.016 20.012 0.008 20.008 20.012 20.01 0.004 20.01 20.012 20.011 0.002 = (2) Bifid(a,b,f) c a + b 2 ¬ flag ¬ 1 flag ¬ 0 a ¬ c min f(a)×f(c) > 0 flag æ ç è ö ÷ ø æ ç è ö ÷ ø while flag ¬ 0 b ¬ c while flag b - a 10- 5 while > c := f(x) 2x 3 3.5 x 2 := + × + 1.9×x - 2.5 Bifid(0, 1,f) = 0.5583267 root(f(x), x) = 0.55833309