computer problems 1.docVIP

数学与信息工程学院 实 验 报 告 课程名称： 计算方法 实 验 室： 5206 实验台号： 19 班 级： 姓 名： 实验日期： 2015 年 3　月 18 日 实验名称 Computer problems 1 实验目的 和 要 求 掌握相对误差，绝对误差的计算，有效数字的控制 实验内容和步骤： 实验内容： Find the approximations to with 8 and 80 significant digits respectively. Compute the absolute error and relative error in approximations of x by . x=,=22/7 (2) x=,=3.14 (3)x=e, =2.718 (4)x=2, =1.414 Use three-digit rounding arithmetic to perform the follwing caculations. (121-0.327)-119 (2) (121-119)-0.327 (3) (-)/(2e-5.4) (4) -10+6e- 4.Let (1) Use four-digit rouding arithmetic to evaluate f(0.1). (2) The actual value is f(0.1)=-1Find the relative error for the value obtained in part(1). 5.Use four-digit rounding arithmetic and the quadratic formulas of Example 1.5.3 to find the most accurate appproximations to the roots of the following quardratic equations .Compute the absolute errors and relative errors. 实验步骤： 1. vpa(7^49,8) ans = 42 vpa(7^49,80) ans = 256923577521058870398046380029443118727168. 2. (1). abs(pi-22/7) ans = 0.0013 abs(pi-22/7)/(22/7) ans = 4.0234e-004 (2). abs(pi-3.14) ans = 0.0016 abs(pi-3.14)/3.14 ans = 5.0721e-004 (3). abs(exp(1)-2.718) ans = 2.8183e-004 abs(exp(1)-2.718)/2.718 ans = 1.0369e-004 (4). abs(sqrt(2)-1.414) ans = 2.1356e-004 abs(sqrt(2)-1.414)/1.414 ans = 1.5103e-004 3. (1). vpa((121-0.327)-119,3) ans = 1.67 (2) vpa((121-119)-0.327,3) ans = 1.67 (3) vpa((13/14-6/7)/(2*exp(1)-5.4),3) ans = 1.95 (4). vpa(-10*pi+6*exp(1)-3/62,3) ans = -15.2 4.(1). x=0.1;y=(x*cos(x)-sin(x))/(x-sin(x));vpa(y,4) ans = -1.999 (2). x=0.1;y=(x*cos(x)-sin(x))/(x-sin(x));z=vpa(y,9);abs(-1z) ans = .96389385362272e-17 5. (1) z=solve(1.002*x^2-11.01*x+0.01165=0),y=vpa(z,4) z = 0.0010582308894024083545001866185885 10.986965721206405974879032747513