电大数值计算方法试题及答案小抄参考

1、专业好文档湖南科技大学考试试题 计算方法 课程 信息、能源 院（系） 07级 通信工程13，电气工程1-4，电子工程12，建筑环境12，自动化12 班级 考试时量 100分钟 命题教师 唐运梅 交题时间： 考试时间：一、选择题（每小题4分，共20分） 1. 误差根据来源可以分为四类，分别是（ a ）a. 模型误差、观测误差、方法误差、舍入误差；b. 模型误差、测量误差、方法误差、截断误差；c. 模型误差、实验误差、方法误差、截断误差；d. 模型误差、建模误差、截断误差、舍入误差。 2. 若，则其六阶差商（ c ）a. 0； b. 1； c. 2； d. 3 。 3. 数值求积公式中的simps

2、on公式的代数精度为 （ d ）a. 0； b. 1； c. 2； d. 3 。 4. 若线性方程组ax = b的系数矩阵a为严格对角占优矩阵，则解方程组的jacobi迭代法和gauss-seidel迭代法 （ b ）a. 都发散；b. 都收敛c. jacobi迭代法收敛，gauss-seidel迭代法发散；d. jacobi迭代法发散，gauss-seidel迭代法收敛。 5. 对于试验方程，euler方法的绝对稳定区间为（ c ）a. ； b. ；c. ； d. ；二、填空题（每空3分，共18分） 1. 已知，则 ， 16 ， 2. 已知，则 f (x)的线性插值多项式为,且用线性插值可得

3、f (7)= 2.6 。3. 要使的近似值的相对误差界小于0.1%，应至少取 4 位有效数字。三、利用下面数据表， 10.466758.030146.042414.425693.12014f (x) (x)2.01.8x 1. 用复化梯形公式计算积分的近似值； 解：1.用复化梯形公式计算 取 1分 2. 用复化simpson公式计算积分的近似值。(要求计算结果保留到小数点后六位). （14分） 解：用复化辛甫生公式计算 取 8分 4、 已知矩阵，求矩阵a的doolittle分解。 （10分） 解：用紧凑格式法 2分 5分 8分 10分5、 用newton迭代法求解方程在2.0

4、附近的实根（计算结果保留到小数点后第四位）。 （12分） 解： ， 6分 8分 ， 11分 故，方程的近似根为1.8974 12分六、对下面线性方程组 （12分） 1.判别用雅可比迭代法是否收敛，若收敛则写出其迭代格式；2.判别用高斯-塞德尔迭代法是否收敛，若收敛则写出其迭代格式；解 1. 雅可比法: 是对角元素为正的实对称阵,下面判别是否同时正定:正定 5分 不正定.即不同时正定 8分 故,jacobi法发散. 9分2. 高斯-塞德尔法:由1知, 是实对称正定矩阵,所以gauss-seidel法收敛. 10分其迭代格式为 12分七、已知初值问题：，取步长h =0.1，1. 用（显式的）eul

5、er方法求解上述初值问题的数值解；2. 用改进的euler方法求上述初值问题的数值解。 （14分）解：1 .建立具体的euler公式: 3分已知，则有： 5分 7分 解：2.建立具体的改进的euler公式: 10分已知则有： 12分 14分 有根祝大家： 好好学习 天天给力if we dont do that it will go on and go on. we have to stop it; we need the courage to do it.his comments came hours after fifa vice-president jeffrey webb - also

6、in london for the fas celebrations - said he wanted to meet ivory coast international toure to discuss his complaint.cska general director roman babaev says the matter has been exaggerated by the ivorian and the british media.blatter, 77, said: it has been decided by the fifa congress that it is a n

7、onsense for racism to be dealt with with fines. you can always find money from somebody to pay them.it is a nonsense to have matches played without spectators because it is against the spirit of football and against the visiting team. it is all nonsense.we can do something better to fight racism and

8、 discrimination.this is one of the villains we have today in our game. but it is only with harsh sanctions that racism and discrimination can be washed out of football.the (lack of) air up there watch mcayman islands-based webb, the head of fifas anti-racism taskforce, is in london for the football

9、associations 150th anniversary celebrations and will attend citys premier league match at chelsea on sunday.i am going to be at the match tomorrow and i have asked to meet yaya toure, he told bbc sport.for me its about how he felt and i would like to speak to him first to find out what his experienc

10、e was.uefa hasopened disciplinary proceedings against cskafor the racist behaviour of their fans duringcitys 2-1 win.michel platini, president of european footballs governing body, has also ordered an immediate investigation into the referees actions.cska said they were surprised and disappointed by

11、 toures complaint. in a statement the russian side added: we found no racist insults from fans of cska.baumgartner the disappointing news: mission aborted.the supersonic descent could happen as early as sunda.the weather plays an important role in this mission. starting at the ground, conditions hav

12、e to be very calm - winds less than 2 mph, with no precipitation or humidity and limited cloud cover. the balloon, with capsule attached, will move through the lower level of the atmosphere (the troposphere) where our day-to-day weather lives. it will climb higher than the tip of mount everest (5.5

13、miles/8.85 kilometers), drifting even higher than the cruising altitude of commercial airliners (5.6 miles/9.17 kilometers) and into the stratosphere. as he crosses the boundary layer (called the tropopause),e can expect a lot of turbulence.the balloon will slowly drift to the edge of space at 120,0

14、00 feet ( then, i would assume, he will slowly step out onto something resembling an olympic diving platform.below, the earth becomes the concrete bottom of a swimming pool that he wants to land on, but not too hard. still, hell be traveling fast, so despite the distance, it will not be like diving

15、into the deep end of a pool. it will be like he is diving into the shallow end.skydiver preps for the big jumpwhen he jumps, he is expected to reach the speed of sound - 690 mph (1,110 kph) - in less than 40 seconds. like hitting the top of the water, he will begin to slow as he approaches the more

16、dense air closer to earth. but this will not be enough to stop him completely.if he goes too fast or spins out of control, he has a stabilization parachute that can be deployed to slow him down. his team hopes its not needed. instead, he plans to deploy his 270-square-foot (25-square-meter) main chute at an altitude of around 5,000 feet (1,524 meters).in order to deploy this chute successfully, he will have to slow to 172 mph (277 kph). he will have a reserve parachute that will open automatical