期
末 统 考 试 卷 A
BB?q?1, √ 选修□ 限修□ 考试形式：闭卷□√ 开卷□ 201- 201学年第 学期 课程代码 课程名称 数值分析 学分 课程性质：必修□
专业班级（教学班） 考试日期 命题教师 系（所或教研室）主任审批签名
1.(20%) Fill in the following blanks. (1) Let 3.(12%) (1) If the norm of the iterative matrix is please poof the following x*=5.3001 be an approximation to x=5.300186, then x*retains _______________ significant x*is __________________. formula:digits,and the relative error of Tx(k)q?x?x(k)?x(k?1) 1?q*?-12?(2) Suppose x?(2,1,?3,4), A??, then x1=__________, A2=___________. ??34?(3) Suppose (2) Let (3) Let f(x)?xex?1 and x0?0.5.Use Newton’s method to find x2. f(x)?xex?1,x0?0.5and x1?0.6.Use the Secant method to find x3. x* is the root of the equation f(x)?0 of multiplicity m(m?2),then the modified x* is______________________________________________. Newton’s iterative formula for finding (4) Let f(x)?x4 and the cubic Lagrange interpolating polynomial for f on the nodes 0,1,2,3 is p3(x). f(x)?p3(x)=_______________________________, and p3(x)=_____________________. 4.(12%) Use the following data to construct an interpolating polynomial Then the error (5) If 'p3(xi)?f(xi) for i?0,1,2,and p3(x1)?f'(x1). p3(x) of the degree three such that f(x)??2x6?3x3?2x?1, then the divided differences f[20,21,?,26]=____________, and f[20,?,27]=_____________. (6) Write an O(h2) three-point formula to approximate f'(x0) by using of f(x0),f(x0?h),f（x0?2h):__________________________________________________. 2.(12%) Establish the Jacobi iterative scheme and Gauss-Seidel iterative scheme for the following linear system: 4x1?2x2?x3?2, 5.(12%) Suppose (a) Determine weight function i 0 1 2 1 2 4 3 2 3 12 xi f(xi) f'(xi) 2x1?6x2?3x3?3,x1?2x2?4x3?5. k?2. w(x)?1,P0(x)?1,P1(x)?x?B1,Pk(x)?(x?Bk)Pk?1?CkPk?2(x) for Test the convergence of the Gauss_Seidel iterative scheme by using the norm of its iterative matrix. ,1] with respect to the B1,B2,C2 such that P0(x),P1(x),P2(x) are orthogonal on [?1w(x). (b) Find the least squares approximating polynomial of degree two for the function f(x)?x4 on the interval [?1,1] 命题教师注意事项:1、主考教师必须于考试一周前将“试卷A”、“试卷B”经教研室主任审批签字后送教务科印刷。 2、请命题教师用黑色水笔工整地书写题目或用A4纸横式打印贴在试卷版芯中。
期
末 统 考 试 卷 A
√ 选修□ 限修□ 考试形式：闭卷□√ 开卷□ 201- 201学年第 学期 课程代码 课程名称 数值分析 学分 课程性质：必修□
专业班级（教学班） 考试日期 命题教师 系（所或教研室）主任审批签名
6.(12%) The Midpoint rule for the approximating ??1f(x)dx gives the value 12,the Composite Midpoint rule f(?1)?f(1) and 1with n?2gives 5,and Composite Simpson’s rule gives 6.Use the fact that f(?0.5)?f(0.5)?1 to determine f(?1),f(?0.5),f(0),f(0.5),f(1). 7.(10%) Determine constant 1a,b,c,dthat will produce a quadrature formula: ''f(x)dx?af(?1)?bf(1)?cf(?1)?df(1) that has degree of 3. ??1 8.(10%) (1)Suppose y'''(t) exists on (a,b).Show that the following two-step explicit scheme w0??0, w1??1,wi?1?wi?y(t0)??0, h?3f(ti,wi)?f(ti?1,wi?1)?,i?1,2,3,?,n?1.2is a scheme of order two to solve the initial value problem for the ordinary differential equation: y(t1)??1,y'(t)?f(t,y),t?[a,b] Where h?b?a,ti?a?ih,i?0,1,2,?,n n命题教师注意事项:1、主考教师必须于考试一周前将“试卷A”、“试卷B”经教研室主任审批签字后送教务科印刷。 2、请命题教师用黑色水笔工整地书写题目或用A4纸横式打印贴在试卷版芯中。