2018年电大计算方法模拟试题及参考答案全参考(4)

1、专业好文档计算方法模拟试题及参考答案模拟试题单项选择题(每小题3 分，共 15 分)1近似值a 4.7860 ，则a2的误差限为()。1112A10 1B.10 222C 1 10 32D.12 10421412. 求积公式f (x)dx 1 f (0) 4 f(1) 1 f(2)的代数精确度为()。0333A.1B.2C.3D.43. 已知 A 43 ，则化为A为对角阵的平面旋转变换角()。32A.B.C.D.4. 设求方程f (x)0的根的切线法收敛，则它具有()敛速。A.线性B.超线性C. 平方D三次5. 欧拉法的局部截断误差阶为()。A. (h)B.(h2 )C. (h3)D.(h4)

2、3 分，共 15 分)1近似值0.02860 102的有效数位为2. 已知 f (x)x3 2x 1 ，则差商f 0,1,23用辛卜生公式计算积分dx。2x4逆幂法是求实方阵的特征值与特征向量的反迭代法。5 计算 a (a 0)的切线法迭代公式为。12 分 ，共 60 分)1已知 1 1, 4 2, 9 3 ， 用抛物插值求3的近似值，并估计误差。2用列主元消元法解方程组2x1 3x2 5x323x1 5x2 8x3 3 x1 3x2 3x323. 用高斯塞德尔迭代法解方程组5x1 2x2 x3 12x1 5x2 2x32x1 2x2 5x31(1) 证明高斯塞德尔迭代法收敛；(2) 写出高斯

3、塞德尔法迭代公式；(3) 取初始值X(0)(0,0,0)T，求出X (1)4. 用双点弦法求方程x3 4x 1 0 的最小正根。(1) 确定含根区间，(2) 检验收敛条件；(3) 写出切线法迭代公式，计算出x1。5. 用予估 -校正法求初值问题y xy y(0) 1在 x 0(0.1)0.2处的解。10 分，每小题5 分)1设Ai (i 0,1, , n)为内插求积公式系数n1证明Ai xi2(b3a3 ) (n 2) 。i022设X (x,xn)T ，证明1 X 2 X X 2。n9参考 答案一、单项选择题（每小题3 分，共 15 分）1 C2. C. .3. A 4. C.5. B二、填空

4、题（每小题3 分，共 15 分）4.按模1. 4 位 .2. 3 .3.2536最小1a5.xn 11 （xna ） （n 0,1,2, ）2xn三、计算题（ 每题 12 分，共 60 分 ）1 作差商表：xiyi一阶差商二阶差商11421395151603 N2(3) 1 1 (3 1)1 (3 1)(3 4) 1.7360533因为 f (x) x, f (x) x 2 , M 388所以，R2(3)M3!3 (3 1)(3 4)(3 9)342. 用列主元法解方程组3x1 5x2 8x3341 x2x33314 x3X (2,1,1)T31）因为2）高斯A 为严格对角占优矩阵，所以高斯-

5、 塞德尔迭代法收敛。- 塞德尔法迭代公式为：(m 1) x1(m)(m)(1 x2 x3 )(m 1) x2x3(m 1)1 (22x1(m 1)2x3(m) ) m 0,1,51(m 1) (m 1)(1x1x2)53）取初值X(0) (0, 0, 0)T，计算得x1(1)1(1)528(1)4251254. 解（1) 由于 f (0) 1 0, f (0.5)0.875 0所以 x0, 0.5xn 1 xn2), f (x) 3x2 4, f (x) 6x,K M22m16, 13KR 1333）双点弦法迭代公式为：(xn xn 1)(xn3 4xn 1)33,(xn 4xn 1) (xn

6、 1 4xn 11)n 1,2,44)取x00.5, x10 ，计算得x10.271512分5 解 因 h 0.1 ， f（x,y） x y，予估 -校正公式得yn(0)11.1yn 0.1xnyn 11.105yn 0.055xnn 0,16分12分再由y0 1 ，计算得y11.105, y2 1.2210255 分，共 10 分）1. 证明设 f (x) x2 ，因为 n 2, R2 (x) 0所以证明所以2i xi2pxdx2xban i12i xax2p x ntwo tries in the Kiwis' 20-18 semi-final win over England,

7、has been passed fit after a lower- leg injury, while Slater has been named at full-back but is still recovering from a knee injury aggravated against USA.Both sides boast 100% records heading into the encounter but Australia have not conceded a try since Josh Charnley's effort in their first poo

8、l match against England on the opening day.Aussie winger Jarryd Hayne is the competition's top try scorer with nine, closely followed by Tuivasa-Sheck with eight.But it is recently named Rugby League International Federation player of the year Sonny Bill Williams who has attracted the most inter

9、est in the tournament so far.The Kiwi - with a tournament high 17 offloads - has the chance of becoming the first player to win the World Cup in both rugby league and rugby union after triumphing with the All Blacks in 2011."I'd give every award back in a heartbeat just to get across the li

10、ne this weekend," saidWilliams. The (lack of) air up thereWatch mCayman Islands-based Webb, the head of Fifa's anti-racism taskforce, is in London for the Football Association's 150th anniversary celebrations and will attend City's Premier League match at Chelsea on Sunday."I a

11、m going to be at the match tomorrow and I have asked to meet Yaya Toure," he told BBC Sport."For me it's about how he felt and I would like to speak to him first to find out what his experience was."Uefa has opened disciplinary proceedings against CSKA for the "racist behavio

12、ur of their fans" duringCity's 2-1 win.Michel Platini, president of European football's governing body, has also ordered an immediate investigation into the referee's actions.CSKA said they were "surprised and disappointed" by Toure's complaint. In a statement the Russ

13、ian 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 be very calm - winds less

14、 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/8.85 kilometers), drifti

15、ng 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 feet (Then, I would assume,

16、 he will slowly step out onto something resembling an Olympic diving platform.They blew it in 2008 when they got caught cold in the final and they will not make the same mistake against the Kiwis in Manchester.Five years ago they cruised through to the final and so far history has repeated itself he

17、re - the last try they conceded was scored by England's Josh Charnley in the opening game of the tournament.That could be classed as a weakness, a team under-cooked - but I have been impressed by the Kangaroos' focus in their games since then.They have been concentrating on the sort of stuff

18、 that wins you tough, even contests - strong defence, especially on their own goal-line, completing sets and a good kick-chase. They've been great at all the unglamorous stuff that often goes unnoticed in the stands but not by your team-mates.It is as though their entire tournament has been preparation for the final.In Johnathan Thurston, Cooper Cronk, Cameron Smith and either Billy Slater or Greg Inglis at full-back they have a spine that is unmatched in rugby league. They have played in so many high-pressure games - a pricele