2018年電大計(jì)算方法模擬試題及參考答案全參考(4)

1、專業(yè)好文檔計(jì)算方法模擬試題及參考答案模擬試題單項(xiàng)選擇題(每小題3 分，共 15 分)1近似值a 4.7860 ，則a2的誤差限為()。1112A10 1B.10 222C 1 10 32D.12 10421412. 求積公式f (x)dx 1 f (0) 4 f(1) 1 f(2)的代數(shù)精確度為()。0333A.1B.2C.3D.43. 已知 A 43 ，則化為A為對(duì)角陣的平面旋轉(zhuǎn)變換角()。32A.B.C.D.4. 設(shè)求方程f (x)0的根的切線法收斂，則它具有()斂速。A.線性B.超線性C. 平方D三次5. 歐拉法的局部截?cái)嗾`差階為()。A. (h)B.(h2 )C. (h3)D.(h4)

2、3 分，共 15 分)1近似值0.02860 102的有效數(shù)位為2. 已知 f (x)x3 2x 1 ，則差商f 0,1,23用辛卜生公式計(jì)算積分dx。2x4逆冪法是求實(shí)方陣的特征值與特征向量的反迭代法。5 計(jì)算 a (a 0)的切線法迭代公式為。12 分 ，共 60 分)1已知 1 1, 4 2, 9 3 ， 用拋物插值求3的近似值，并估計(jì)誤差。2用列主元消元法解方程組2x1 3x2 5x323x1 5x2 8x3 3 x1 3x2 3x323. 用高斯塞德爾迭代法解方程組5x1 2x2 x3 12x1 5x2 2x32x1 2x2 5x31(1) 證明高斯塞德爾迭代法收斂；(2) 寫出高斯

3、塞德爾法迭代公式；(3) 取初始值X(0)(0,0,0)T，求出X (1)4. 用雙點(diǎn)弦法求方程x3 4x 1 0 的最小正根。(1) 確定含根區(qū)間，(2) 檢驗(yàn)收斂條件；(3) 寫出切線法迭代公式，計(jì)算出x1。5. 用予估 -校正法求初值問(wèn)題y xy y(0) 1在 x 0(0.1)0.2處的解。10 分，每小題5 分)1設(shè)Ai (i 0,1, , n)為內(nèi)插求積公式系數(shù)n1證明Ai xi2(b3a3 ) (n 2) 。i022設(shè)X (x,xn)T ，證明1 X 2 X X 2。n9參考 答案一、單項(xiàng)選擇題（每小題3 分，共 15 分）1 C2. C. .3. A 4. C.5. B二、填空

4、題（每小題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、計(jì)算題（ 每題 12 分，共 60 分 ）1 作差商表：xiyi一階差商二階差商11421395151603 N2(3) 1 1 (3 1)1 (3 1)(3 4) 1.7360533因?yàn)?f (x) x, f (x) x 2 , M 388所以，R2(3)M3!3 (3 1)(3 4)(3 9)342. 用列主元法解方程組3x1 5x2 8x3341 x2x33314 x3X (2,1,1)T31）因?yàn)?）高斯A 為嚴(yán)格對(duì)角占優(yōu)矩陣，所以高斯-

5、 塞德爾迭代法收斂。- 塞德爾法迭代公式為：(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，計(jì)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）雙點(diǎn)弦法迭代公式為：(xn xn 1)(xn3 4xn 1)33,(xn 4xn 1) (xn

6、 1 4xn 11)n 1,2,44)取x00.5, x10 ，計(jì)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 ，計(jì)算得y11.105, y2 1.2210255 分，共 10 分）1. 證明設(shè) f (x) x2 ，因?yàn)?n 2, R2 (x) 0所以證明所以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