1、中國計量學院2008 2009 學年第 1 學期計算方法課程考試試卷（A ）1. Using Newtons method to find the solution accurate to within 10-3 to the following problem., on -3,-2Solution: (3 %) (3%) (3%)n0-3-11-2.88888889-0.072702322-2.88079976-0.010756343-2.87938672-0.00001123(7%)2. (16%) For the given functions , let , and . Constru

2、ct the Lagrange interpolating polynomials of degree 2 to approximate .Solution:(5%) (5%) (6%)3. Approximate the following integral using Gaussian quadrature with n = 3 and Simpsons rule, and compare the results.Solution: (6%) The solution accurate to within 10-7 is 0.9460831. Gaussian quadrature wit

3、h n = 3 is more accurate than Simpsons rule. (4%)4. Use the Runge-Kutta method of 4 to approximate the solution to the following initial-value problem, and compare the results to the actual values. () with y(0) = 1.Solution: (R-K 4)0.21.202471.2024609550.41.418731.41872 (8%) (6%) (2%)5. Solve the fo

4、llowing linear system by LU matrix factorization with Doolittle form.Solution: (5%) (5%) (6%) 6. Given the following linear system(a) Use SOR method with (Gauss-Seidel) and to solve above linear system with x(0)= (1,1,1) to the fifth step.(b) Show the convergence of the SOR method.(c) Seek the optional choice of for the SOR method.Solution:(a) GaussSeidel (10%) GaussSeidel, x(0)= (1,1,1)Tk011115.2500003.81250-5.04687523.14062503.8828125-5.029296933.08789063.9267578-