電大數(shù)值計(jì)算方法試題及答案小抄參考

1、湖南科技大學(xué)考試試題 計(jì)算方法 課程 信息、能源 院（系） 07級(jí) 通信工程13，電氣工程1-4，電子工程12，建筑環(huán)境12，自動(dòng)化12 班級(jí) 考試時(shí)量 100分鐘 命題教師 唐運(yùn)梅 交題時(shí)間： 考試時(shí)間：一、選擇題（每小題4分，共20分） 1. 誤差根據(jù)來(lái)源可以分為四類，分別是（ a ）a. 模型誤差、觀測(cè)誤差、方法誤差、舍入誤差；b. 模型誤差、測(cè)量誤差、方法誤差、截?cái)嗾`差；c. 模型誤差、實(shí)驗(yàn)誤差、方法誤差、截?cái)嗾`差；d. 模型誤差、建模誤差、截?cái)嗾`差、舍入誤差。 2. 若，則其六階差商（ c ）a. 0； b. 1； c. 2； d. 3 。 3. 數(shù)值求積公式中的simpson公式的

2、代數(shù)精度為 （ d ）a. 0； b. 1； c. 2； d. 3 。 4. 若線性方程組ax = b的系數(shù)矩陣a為嚴(yán)格對(duì)角占優(yōu)矩陣，則解方程組的jacobi迭代法和gauss-seidel迭代法 （ b ）a. 都發(fā)散；b. 都收斂c. jacobi迭代法收斂，gauss-seidel迭代法發(fā)散；d. jacobi迭代法發(fā)散，gauss-seidel迭代法收斂。 5. 對(duì)于試驗(yàn)方程，euler方法的絕對(duì)穩(wěn)定區(qū)間為（ c ）a. ； b. ；c. ； d. ；二、填空題（每空3分，共18分） 1. 已知，則 ， 16 ， 2. 已知，則 f (x)的線性插值多項(xiàng)式為,且用線性插值可得f (7)

3、= 2.6 。3. 要使的近似值的相對(duì)誤差界小于0.1%，應(yīng)至少取 4 位有效數(shù)字。三、利用下面數(shù)據(jù)表， 10.466758.030146.042414.425693.12014f (x) (x)2.01.8x 1. 用復(fù)化梯形公式計(jì)算積分的近似值； 解：1.用復(fù)化梯形公式計(jì)算 取 1分 2. 用復(fù)化simpson公式計(jì)算積分的近似值。(要求計(jì)算結(jié)果保留到小數(shù)點(diǎn)后六位). （14分） 解：用復(fù)化辛甫生公式計(jì)算 取 8分 4、 已知矩陣，求矩陣a的doolittle分解。 （10分） 解：用緊湊格式法 2分 5分 8分 10分5、 用newton迭代法求解方程在2.0附近的實(shí)根

4、（計(jì)算結(jié)果保留到小數(shù)點(diǎn)后第四位）。 （12分） 解： ， 6分 8分 ， 11分 故，方程的近似根為1.8974 12分六、對(duì)下面線性方程組 （12分） 1.判別用雅可比迭代法是否收斂，若收斂則寫(xiě)出其迭代格式；2.判別用高斯-塞德?tīng)柕ㄊ欠袷諗?，若收斂則寫(xiě)出其迭代格式；解 1. 雅可比法: 是對(duì)角元素為正的實(shí)對(duì)稱陣,下面判別是否同時(shí)正定:正定 5分 不正定.即不同時(shí)正定 8分 故,jacobi法發(fā)散. 9分2. 高斯-塞德?tīng)柗?由1知, 是實(shí)對(duì)稱正定矩陣,所以gauss-seidel法收斂. 10分其迭代格式為 12分七、已知初值問(wèn)題：，取步長(zhǎng)h =0.1，1. 用（顯式的）euler方法求

5、解上述初值問(wèn)題的數(shù)值解；2. 用改進(jìn)的euler方法求上述初值問(wèn)題的數(shù)值解。 （14分）解：1 .建立具體的euler公式: 3分已知，則有： 5分 7分 解：2.建立具體的改進(jìn)的euler公式: 10分已知?jiǎng)t有： 12分 14分 有根祝大家： 好好學(xué)習(xí) 天天給力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 in lo

6、ndon 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 nonsen

7、se 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 disc

8、rimination.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 assoc

9、iations 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 experience was

10、.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 tour

11、es 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 have to

12、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 miles

13、/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 120,000 fe

14、et ( 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 into

15、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 dense

16、 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 automaticall