中国石油大学计算方法模拟试题
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第一章测试1.数值计算方法研究的误差有()A:截断误差;B:观测误差;C: 模型误差;D:舍入误差.答案:AD2.A:只有模型误差、截断误差与观测误差。
B: 只有舍入误差、截断误差与观测误差;C:只有模型误差、观测误差与舍入误差;D:只有模型误差、截断误差与舍入误差;答案:C3.A:4位B:5位C:3位D:2位答案:A4.对于下列表达式,用浮点数运算,精度较高是A:B:C:D:答案:A5.A:B:C:D:答案:B第二章测试1.A:0.5000B:0.6250C:0.5625D:0.6875答案:C2.A:B:C:D:答案:CD3.关于Steffensen(斯蒂芬森)迭代方法,下列命题中正确的是:A:Steffensen迭代法使得收敛的迭代格式加速收敛,发散的迭代格式更快发散。
B:Steffensen迭代法使得某些发散的迭代格式变为收敛。
C:Steffensen迭代法使得任何收敛的迭代格式加速收敛。
D:Steffensen迭代法使得某些收敛的迭代格式加速收敛。
答案:BD4.关于Newton迭代法,下列命题中正确的是:A:求解任一方程的Newton迭代法都是2阶收敛的。
B:Newton迭代格式若收敛,则一定是超线性收敛的。
C:D:Newton迭代格式可能收敛也可能发散。
答案:CD5.A:6B:3C:5D:4答案:A第三章测试1.A:若求解失败,则说明矩阵A奇异。
B:算法的计算量与近似成正比。
C:若A的对角线元素的绝对值都大于1,则求解结果的精度一定较高。
D:只要A非奇异,则求解结果的精度一定较高。
答案:B2.列主元Gauss消去法与Gauss顺序消元法相比,优点是:A:提高了稳定性,减少了误差的影响。
B:方程组的系数矩阵奇异时也可以求解。
C:能求出方程组的精确解。
D:减少了计算量。
答案:A3.A:平方根法与Gauss列主元消去法相比,提高了稳定性,但增加了计算量。
B:只要是对称正定矩阵,就可用平方根法求解。
第三章3.1整数四则运算【题目描述】小明上小学一年级了,老师已经教会了他们进行整数的+、-、*、/、%计算,下面老师开始出题,给出一个简单的算术表达式,请小明给出计算结果。
【输入】接受两个整数,每个整数之间使用空格分隔。
【输出】分别输出进行+、-、*、/、*之后的运行结果。
【样例输入】10 3【样例输出】10+3=13 10-3=7 10*3=30 10/3=3 10%3=1注:为了输出一个%符号,在控制字符串中需要写成%%,这是因为%在控制字符串中有特殊含义3.2美元与人民币【题目描述】美元越来越贬值了,手上留有太多的美元似乎不是件好事。
赶紧算算你的那些美元还值多少人民币吧。
假设美元与人民币的汇率是1美元兑换6.5573元人民币,编写程序输入美元的金额,输出能兑换的人民币金额。
【输入】美元的金额。
【输出】能兑换的人民币的数值。
输出保留2位小数。
【样例输入】100【样例输出】655.733.3计算月收入【题目描述】CoCo的表姐刚从大学毕业,进入到一家小型外贸公司工作。
该公司员工月收入的计算方法为:月基本工资加当月提成。
从键盘输入CoCo表姐某月的基本工资和该月的提成,计算并输出表姐该月的收入。
【输入】输入两个数分别代表月基本工资和月提成。
【输出】计算并输出月收入,保留2位小数。
【样例输入】3150.2 1200【样例输出】4350.203.4求整数均值【题目描述】计算4个整数的和与平均值。
题目保证输入与输出均在整型范围内。
【输入】4个整数,其间以空格分隔。
【输出】按照格式顺序输出和与平均值,其中平均值精确到小数点后1位。
【输入样例】1 2 3 4【输出样例】Sum = 10; Average = 2.53.5简单加密【题目描述】信息时代最怕的就是个人信息泄密。
你现在已经掌握了一些技能,那么就尝试着对信息进行一些简单的加密吧!现在从键盘输入任意两个字母,要求对它们进行加密。
规则是:用原字母后的第3个字母来代替。
本套模拟题包含《数学》《英语》《计算机》三个科目中国石油大学(北京)入学测试机考专升本高等数学模拟题1、题目Z1-2(2)()A.AB.BC.CD.D标准答案:A2、题目20-1:(2)()A.AB.BC.CD.D标准答案:A3、题目20-2:(2)()A.AB.BC.CD.D标准答案:B4、题目20-3:(2)()A.AB.BC.CD.D标准答案:A5、题目20-4:(2)()A.AB.BC.CD.D标准答案:D6、题目20-5:(2)()A.AB.BC.CD.D标准答案:D7、题目20-6:(2)()A.AB.BC.CD.D标准答案:A8、题目20-7:(2)()A.AB.BC.CD.D标准答案:D9、题目20-8:(2)()A.AB.BC.CD.D标准答案:C10、题目11-1(2)()A.AB.BC.CD.D标准答案:C11、题目11-2(2)()A.AB.BC.CD.D标准答案:B12、题目11-3(2)()A.AB.BC.CD.D标准答案:A13、题目20-9:(2)()A.AB.BC.CD.D标准答案:C14、题目11-4:(2)()A.AB.BC.CD.D标准答案:D15、题目11-5(2)()A.AB.BC.CD.D标准答案:C16、题目20-10:(2)()A.AB.BC.CD.D标准答案:B17、题目11-6(2)()A.AB.BC.CD.D标准答案:B18、题目11-7(2)()A.AB.BC.CD.D标准答案:C19、题目11-8(2)()A.AB.BC.CD.D标准答案:C20、题目11-9(2)()A.AB.BC.CD.D标准答案:D21、题目11-10(2)()A.AB.BC.CD.D标准答案:B22、题目19-1:(2)()A.AB.BC.CD.D标准答案:C23、题目19-2:(2)()A.AB.BC.CD.D标准答案:B24、题目19-3:(2)()A.AB.BD.D标准答案:D25、题目12-1(2)()A.AB.BC.CD.D标准答案:D26、题目12-2(2)()A.AB.BC.CD.D标准答案:D27、题目19-4:(2)()A.AB.BC.CD.D标准答案:B28、题目12-3(2)()B.BC.CD.D标准答案:B29、题目12-4(2)()A.AB.BC.CD.D标准答案:C30、题目12-5(2)()A.AB.BC.CD.D标准答案:A31、题目19-5:(2)()A.AB.BC.C标准答案:C32、题目12-6(2)()A.AB.BC.CD.D标准答案:A33、题目12-7(2)()A.AB.BC.CD.D标准答案:B34、题目19-6:(2)()A.AB.BC.CD.D标准答案:B35、题目12-8(2)()A.AB.BC.CD.D标准答案:B36、题目19-7:(2)()A.AB.BC.CD.D标准答案:B37、题目12-9(2)()A.AB.BC.CD.D标准答案:A38、题目12-10(2)()A.AB.BC.CD.D标准答案:C39、题目19-8:(2)()A.AB.BC.CD.D标准答案:D40、题目19-9:(2)()A.AB.BC.CD.D标准答案:A41、题目19-10:(2)()A.AB.BC.CD.D标准答案:C42、题目18-1:(2)()A.AB.BC.CD.D标准答案:A43、题目18-2:(2)()A.AB.BC.CD.D标准答案:C44、题目18-3:(2)()A.AB.BC.CD.D标准答案:D45、题目13-1(2)()A.AB.BC.CD.D标准答案:D46、题目18-4:(2)()A.AB.BC.CD.D标准答案:A47、题目13-2(2)()A.AB.BC.CD.D标准答案:B48、题目13-3(2)()A.AB.BC.CD.D标准答案:D49、题目18-5:(2)()A.AB.BC.CD.D标准答案:D50、题目13-4(2)()A.AB.BC.CD.D标准答案:B51、题目13-5(2)()A.AB.BC.CD.D标准答案:D52、题目18-6:(2)()A.AB.BC.CD.D标准答案:B53、题目13-6(2)()A.AB.BC.CD.D标准答案:C54、题目13-7(2)()A.AB.BC.CD.D标准答案:C55、题目18-7:(2)()A.AB.BC.CD.D标准答案:B56、题目18-8:(2)()A.AB.BC.CD.D标准答案:B57、题目13-8(2)()A.AB.BC.CD.D标准答案:B58、题目13-9(2)()A.AB.BC.CD.D标准答案:C59、题目18-9:(2)()A.AB.BC.CD.D标准答案:B60、题目13-10(2)()A.AB.BC.CD.D标准答案:A61、题目18-10:(2)()A.AB.BC.CD.D标准答案:A62、题目17-1:(2)()A.AB.BC.CD.D标准答案:C63、题目17-2:(2)()A.AB.BC.CD.D标准答案:D64、题目17-3:(2)()A.AB.BC.CD.D标准答案:C65、题目17-4:(2)()A.AB.BC.CD.D标准答案:A66、题目17-5:(2)()A.AB.BC.CD.D标准答案:D67、题目14-1(2)()A.AB.BC.CD.D标准答案:D68、题目14-2(2)()A.AB.BC.CD.D标准答案:A69、题目17-6:(2)()A.AB.BC.CD.D标准答案:B70、题目14-3(2)()A.AB.BC.CD.D标准答案:D71、题目17-7:(2)()A.AB.BC.CD.D标准答案:B72、题目14-4(2)()A.AB.BC.CD.D标准答案:C73、题目14-5(2)()A.AB.BC.CD.D标准答案:C74、题目17-8:(2)()A.AB.BC.CD.D标准答案:D75、题目14-7(2)()A.AB.BC.CD.D标准答案:A76、题目14-8(2)()A.AB.BC.CD.D标准答案:D77、题目17-9:(2)()A.AB.BC.CD.D标准答案:B78、题目14-9(2)()A.AB.BC.CD.D标准答案:C79、题目14-10(2)()A.AB.BC.CD.D标准答案:A80、题目17-10:(2)()A.AB.BC.CD.D标准答案:C81、题目16-1:(2)()A.AB.BC.CD.D标准答案:D82、题目16-2:(2)()A.AB.BC.CD.D标准答案:B83、题目16-3:(2)()A.AB.BC.CD.D标准答案:C84、题目15-1(2)()A.AB.BC.CD.D标准答案:C85、题目15-2(2)()A.AB.BC.CD.D标准答案:C86、题目16-4:(2)()A.AC.CD.D标准答案:D87、题目15-3(2)()A.AB.BC.CD.D标准答案:D88、题目15-4(2)()A.AB.BC.CD.D标准答案:B89、题目15-5(2)()A.AB.BC.CD.D标准答案:B90、题目15-6(2)()B.BC.CD.D标准答案:A91、题目15-7(2)()A.AB.BC.CD.D标准答案:C92、题目15-8(2)()A.AB.BC.CD.D标准答案:C93、题目16-5:(2)()A.AB.BC.CD.D标准答案:A94、题目15-9(2)()A.AB.BC.CD.D标准答案:B95、题目15-10(2)()A.AB.BC.CD.D标准答案:D96、题目16-6:(2)()A.AB.BC.CD.D标准答案:B97、题目16-7:(2)()A.AB.BC.CD.D标准答案:C98、题目16-8:(2)()A.AB.BC.CD.D标准答案:B99、题目16-9:(2)()A.AB.BC.CD.D标准答案:A100、题目16-10:(2)()A.AB.BC.CD.D标准答案:D中国石油大学(北京)入学测试机考专升本英语模拟题1、One of my teeth is so ______ that it is going to be missing soon(2)()A.loseB.looseC.lossD.lost标准答案:B2、—How about taking a walk?—Oh, I think it’s ______ cold for a walk(2)()A.very muchB.too muchC.much tooD.so much标准答案:C3、You are supposed to write your composition every ______ line.(2)()A.oneB.aC.otherD.another标准答案:C4、After living for years in a big city, they found it difficult to settle ______ in a town.(2)()A.forB.atC.upD.down标准答案:D5、The reason for my absence was ______ I had fallen ill.(2)()A.whyB.becauseC.forD.that标准答案:D6、This is the university ______.(2)()A.at which do we studyB.we are studyingC.we are studying atD.where we study at标准答案:A7、It was in this house ______ the important meeting in history was held.(2)()A.whereB.thatC.whichD.in which标准答案:B8、She looked so honest that we all regarded her story ______.(2)()A.like trueB.as trueC.like realD.as real标准答案:B9、Mrs. Brown as well as her children ______ to go Paris on holiday next week.(2)()A.isB.areC.willD.will be标准答案:A10、He is training hard, hoping to ______ a new world record.(2)()A.set offB.set asideC.set upD.set out标准答案:C11、___in the arguments about the morality of artificially reproducing life is the fact that,at present, cloning is a very inefficient procedure.(2)()A.OverlookedB.OverlookingC.Having overlookedD.Having been overlooked标准答案:B12、We’ll___ what our country expects of us.(2)()A.keep up withB.put up withC.stand up toD.live up to标准答案:D13、The writer has listed why cloning is not feasible to be ___on humans.(2)()A.amendedB.adoptedC.adjustedD.adapted标准答案:B14、He was a charming and ___host whose house was an___rendezvous( 集合的) of the great.(2)()A.accomplished, acceptedB.accomplishing, acceptingC.accomplishing, acceptedD.accomplished, accepting标准答案:A15、I think the chief thing that ___ me about Mr. Bush was his kindness and humor.(2)()A.hitB.struckC.beatD.knocked标准答案:B16、Mrs. Clinton was always neatly and quietly dressed ___ her age and status.(2)()A.in regard toB.in accordance withC.in reference toD.in comparison with标准答案:B17、We discussed only such problems ___ concerned everyone of us.(2)()A.thatB.whatC.asD.whether标准答案:A18、After the ___of 17 British passengers, Mr. Blair continued to express his concern over the safety of the other passengers still on board the hijacked airliner.(2)()A.relayB.releaseC.conveyD.transfer标准答案:B19、The “quality” newspapers are often held ___ as an example of impartial journalism.(2)()A.backB.inC.upD.onto标准答案:C20、At the age of 14, he went to his uncle's farm, where he had lessons on botany ___ .(2)()A.self-taughtB.self-teachingC.being self-taughtD.having self-taught标准答案:B21、He can't drive a car. Let ___fly an aero-plane.(2)()A.solitaryB.lonelyC.aloneD.loneliness标准答案:C22、The boy said to his mother in an ___ voice that she shouldn't have blamed him.(2)()A.injuryB.injuriousC.injuredD.injuring标准答案:D23、___how the splendid Maya Culture disappeared all of a sudden from the earth, it remains a mystery hard to solve.(2)()A.In turnB.As toC.Thanks toD.As a rule标准答案:B24、In the era of market economy, the concept of “Consumer First” should be ___by manufacturers.(2)()A.rejectedB.reformedC.relivedD.reinforced标准答案:D25、He's widely known more ___a poet than ___a novelist.(2)()A.for,toB.for,asC.as,forD.as,as标准答案:D26、The football match was held over until further notice ___the continual rain.(2)()A.on account ofB.thanks toC.but forD.as for标准答案:B27、The rain was heavy and ___the land was flooded.(2)()A.consistentlyB.consequentlyC.constantlyD.continuously标准答案:B28、Another issue ___the new republic is the problem of the education of its citizens.(2)()A.confiningB.confirmingC.confrontingD.contributing标准答案:C29、A window in the kitchen room was ___; there was rubbish everywhere and the clock had been stolen.(2)()A.scatteredB.smashedC.scratchedD.scraped标准答案:B30、Knowing that her son was suffering from a ___ disease, the mother cried her eyes out.(2)()A.deadlyB.dyingC.dead-likeD.deathly标准答案:A31、Some people consider it unwise to ___themselves in a quarrel between husband and wife.(2)()A.participateB.involveC.combineD.associate标准答案:B32、I have just come here to see if I can be___ to you.(2)()A.helpB.of helpC.with helpD.for help标准答案:B33、Imagine ___with someone who never stops ___practical jokes on you.(2)()A.to live, to playB.to live, playingC.living, to playD.living, playing标准答案:B34、The Old Man and the Sea and many other novels ___ Ernest Hemingway the Nobel Prize for Literature in 1954.(2)()A.earnedB.gainedC.awardedD.claimed标准答案:A35、Those who had moved to America under the ___that America was paved with gold everywhere started to regret their decision.(2)()A.illusionB.intentionC.impressionD.concept标准答案:A36、___change your mind,please give us a call.(2)()A.Were you toB.Would youC.Could youD.Might you标准答案:A37、When ___, he denied ___ anything illegal.(2)()A.questioned, doingB.being questioned, doingC.questioning, doingD.questioning, having done标准答案:B38、See you later. Jenny. I'm glad ___ with you for six months.(2)()A.to workB.to be workingC.to have workedD.to having been working标准答案:C39、The girl in the snapshot was smiling sweetly, her long hair___________in the breeze.(2)()A.flowedB.had flowedC.flowingD.was flowing标准答案:A40、___from the European continent, England had been in close contact with the outside world.(2)()A.Because cutting offB.While to be cut offC.Although cut itself offD.Even if cut off标准答案:D41、The actors have to ___ before they appear in front of the audience.(2)()A.cover upB.paint upC.make upD.do up标准答案:C42、Quite a lot of people watch TV only to ___time.(2)()A.passB.killC.wasteD.spend标准答案:A43、John was never particular ___ the food his wife served.(2)()A.aboutB.ofC.forD.to标准答案:A44、The designing of a satellite in the heavy environment is ___an easy job.(2)()A.by all meansB.by means ofC.by no meansD.by any means标准答案:C45、Edward is the boy ___I think scored the winning point for the basketball team.(2)()A.thatB.whatC.whomD.who标准答案:D46、It is often more difficult to find trained men than ___for scientific research.(2)()A.getting financial supportB.to get financial supportC.get financial supportD.in getting financial support标准答案:B47、John is a good student, ___his best subject.(2)()A.as EnglishB.being EnglishC.English asD.English being标准答案:D48、___great was the destruction that the South took decades to recover.(2)()A.VeryB.TooC.SoD.Such标准答案:C49、You ought not to ___him the news that day.(2)()A.tellB.be tellingC.have been toldD.have told标准答案:D50、Hot metal ___as it grows cooler.(2)()A.contractsB.reducesC.condensesD.decreases标准答案:A51、Do you have a preference ___a particular food?(2)()A.withB.atC.forD.in标准答案:C52、By now most freshmen have grown so used to university life that they have forgotten all those___ about the university they originally had.(2)()A.concernsB.worryC.dreamsD.ambition标准答案:C53、Many people want to buy it because.___. the price is reasonable; ___ , it's rather durable.(2)()A.on one side, on the other sideB.for one thing, for anotherC.on the one hand, on the other handD.in one part, in the other part标准答案:C54、The proposal ___we start doing the experiment two days earlier has been agreed upon by all.(2)()A.whichB.whatC.thatD.of which标准答案:C55、Spring ___, we may look forward to better weather.(2)()A.comesB.has comeC.to be comingD.having come标准答案:C56、The purpose of the research had a more different meaning for them than___ .(2)()A.for ours it hadB.it did for usC.with usD.with ours标准答案:B57、___from the balcony when he saw a policeman approaching him.(2)()A.Jumped down the thiefB.Down the thief jumpedC.Down jumped the thiefD.Down did the thief jump标准答案:C58、Can you see a man and his horse ___are crossing the bridge?(2)()A.whoB.whichC.thatD.all标准答案:C59、___, I cannot agree with him on the matter.(2)()A.Much as I respect himB.More as I respect himC.As I respect him muchD.As I respect him more标准答案:A60、But for your help, we ___the work as scheduled.(2)()A.could not finishB.would not have finishedC.would have finishedD.could have finished标准答案:B61、Do you know ___the population of China is?(2)()A.how manyB.how muchC.whichD.what标准答案:B62、Advertising is different from other forms of communication___the advertiser pays for the message to be delivered.(2)()A.in thatB.now thatC.see thatD.whereas标准答案:A63、I know nothing about his journey ___ he is likely to be away for six months.(2)()A.exceptB.unlessC.except thatD.apart from标准答案:C64、___editor and ___publisher of this magazine is a learned man from Britain.(2)()A.An, aB.The, aC.The, theD.The, /标准答案:D65、Many a white-collar worker___to return to the easy days of university or college.(2)()A.wishesB.wishC.have wishedD.wishing标准答案:A66、Would you like him to paint it blue?I'd rather he ___it green.(2)()A.paintsB.paintedC.paintD.is painting标准答案:C67、James dressed himself up as a plumber before leaving the house lest he ___.(2)()A.was recognizedB.could be recognizedC.should be recognizedD.was being recognized标准答案:C68、He struck the girl in the face and she fell to the ground ___.(2)()A.dieB.deathC.deadD.deadly标准答案:C69、I think it quite essential that your child ___ a foreign language at school.(2)()A.must learnB.learnsC.learnedD.learn标准答案:D70、She woke up from the nightmare ___ .(2)()A.with startB.with a startC.startingD.started标准答案:B71、Is there any___in your company?(2)()A.vacancyB.desertionC.emptinessD.hollow标准答案:A72、The old man ___the boy on his knees.(2)()A.seatedB.was seatedC.satD.was sat标准答案:A73、V oices of argument were ___as the two motorists became more bad-tempered.(2)()A.increasedB.risenC.swollenD.raised标准答案:D74、Don't take him for a friend; he's ___a bully.(2)()A.everything toB.nothing butC.anything likeD.something of标准答案:D75、She was exhausted and in no___for dancing.(2)()A.emotionB.temperC.moodD.feeling标准答案:C76、During foggy weather trains are late ___ .(2)()A.and so forthB.more often than notC.or somethingD.as a matter of fact标准答案:B77、The paint is still wet___.(2)()A.Don't he sure to touch it.B.Not be sure to touch it.C.Be not sure to touch it.D.Be sure not to touch it.标准答案:D78、Who will be in charge of your team?We'll elect ___ .(2)()A.Henry as captainB.Henry captainC.captain HenryD.as captain Henry标准答案:A79、The speaker doesn't know how to ___himself across.(2)()A.makeB.runC.takeD.put标准答案:D80、It's high time you ___us the truth.(2)()A.tellB.have toldC.toldD.had told标准答案:C81、If I___to do the experiment, I would do it some other way.(2)()A.should beB.should be goingC.wasD.were标准答案:D82、I would not be home tonight___ you not___me a lift in your car.(2)()A.if, giveB.if had, givenC.had, givenD.have, given标准答案:C83、We___it without your help.(2)()A.couldn't have doneB.couldn't doC.could have doneD.could haven't done标准答案:A84、___in the crash, he won't participate in the race.(2)()A.His broken legB.His leg is brokenC.His leg having been brokenD.His leg being broken标准答案:C85、So fast ___that it is difficult for us to imagine its speed.(2)()A.light travelsB.travels lightC.does light travelD.has light traveled标准答案:C86、Is this film moving?Yes, it is___.(2)()A.Rarely have I seen this before.B.Rarely before have I seen this.C.Rarely have I seen before this.D.Rarely I have seen this before.标准答案:A87、I suppose she is not serious,___ ?(2)()A.do IB.don't IC.isn't sheD.is she标准答案:C88、I can only do it for you ___I'm paid in advance.(2)()A.just asB.in thatC.now thatD.on condition that标准答案:D89、Whatever is worth ___ at all is worth ___well.(2)()A.doing, being doneB.doing, doingC.being done, doingD.being done, being done标准答案:A90、You'll see to it ___everything is ready in time.(2)()A.whatB.thatC.whetherD.how标准答案:B91、How well educated a person is ___a strong influence on his career.(2)()A.hasB.haveC.to haveD.having标准答案:A92、What he wrote made no ___to me.(2)()A.meaningB.ideaC.senseD.story标准答案:C93、I bought this antique vase at a quite ___price.(2)()A.cheapB.reasonableC.expensiveD.small标准答案:B94、___change your mind, please give me a call.(2)()A.Might youB.Were youC.Should youD.Would you标准答案:C95、Hardly had they arrived at the airport ___the plane started to leave.(2)()A.thanB.thenC.untilD.when标准答案:C96、This project must be completed ___as scheduled.(2)()A.in vainB.at mostC.in advancedD.by all means标准答案:C97、___the people in the workshop, Tonny is the most skilled.(2)()A.Of allB.To allC.In allD.From all标准答案:A98、Jane cannot drive us downtown, for she has ___to take us all.(2)()A.very small a carB.too small a carC.so a small carD.such small a car标准答案:B99、When questioned, he ___doing anything illegal.(2)()A.refusedB.objectedC.deniedD.opposed标准答案:C100、The car___on the way to the station, and we had to get a taxi.(2)()A.broke downB.breaking downC.broken downD.was broken down标准答案:C中国石油大学(北京)入学测试机考专升本计算机应用基础模拟题1、Windows 的主要特点是___。
《数学物理方法》试卷专业班级姓名学号开课系室计算数学系考试日期 2014年 1 月10 日注意事项:(1)答卷时请保持卷面清晰,整洁;(2)请在试卷本正面答题,反面及附页可做草稿纸;(3)本试卷共七页,满分100分;(4)试卷本请勿撕开,否则作废.一、选择题(本题共5小题,每小题3分,共15分)在下列每小题的4个备选项中,只有一项是最符合题意的,请将代码(A 、B 、C 、D )填在题后相应的括号内。
1、偏微分方程与初始条件结合在一起,统称为( ).(A) 定解问题; (B) 柯西问题; (C) 边值问题; (D) 以上均不正确.2、下列偏微分方程中,属于二阶、线性、非齐次的是( ).(A) 2260u u u u t x ∂∂++-=∂∂; (B) 2222cos 40∂+-⋅-=∂u t t u x x ; (C) 290∂⎛⎫+-= ⎪∂⎝⎭u xu t t ; (D) 2260∂∂+⋅-⋅=∂∂t u u e xt u x t .3、在xoy 平面上,方程22222290u u ux x y y∂∂∂-+=∂∂∂∂为( ).(A)椭圆型; (B)双曲型; (C)抛物型; (D)混合型.4、 不等式312z z ->-所确定的区域的图形为( ). (A)无界单连通区域; (B)有界多连通区域; (C) 有界单连通区域; (D) 无界多连通区域.5、设()(,)(,)f z u x y iv x y =+,那么(,)u x y 与(,)v x y 在点()00,x y 可微是()f z 在点000z x iy =+可微的( ).(A)充分但非必要条件; (B)必要但非充分条件; (C)充分必要条件; (D)既非充分也非必要条件.二、填空题(本题共5小题,每题3分,共15分) 请将正确答案填在题后相应的横线上。
1、 对如下偏微分方程222222320u u u uu x x y y x∂∂∂∂+-++=∂∂∂∂∂ 写出其特征方程 .2、函数在()2f z z =在z 平面上是否解析(“是”或“否”) .3、由贝塞尔函数的递推公式有 =)(0x J dxd.4、一根具有绝热侧表面的均匀细杆,它的初始温度为()f x ,一端0x =温度为()p t ,另一端x l =绝热,写出热过程的定解问题_________________________________________________. 5、i 31--的指数表达形式: .三、计算题(本题20分)1. (5分)⎰=+-3||2d )2()1(e z zz z z2. (5分)122cos (1)Z zdz z z =-⎰3、(10分)已知解析函数v u z f i )(+=的实部y x y u 233-=,求函数v u z f i )(+=的表达式,并使0)0(=f .四、计算题(本题15分) 利用特征函数法求定解问题()2222cos 0<,00 0,00 0x x l u u x a A x l t t x l uu t x x u x x l π==⎧∂∂-=<>⎪∂∂⎪∂∂⎪==≥⎨∂∂⎪⎪=≤≤⎪⎩.五、计算题(本题10分)利用拉普拉斯积分变换法求解下列定解问题:(已知()11nn n L t p+Γ+⎡⎤=⎣⎦) ()()226,0 ,010,0y uxx y x y u x x u y e y -⎧∂=-∞<<+∞>⎪∂∂⎪⎪=-∞<<+∞⎨⎪=>⎪⎪⎩六、计算题(本题15分) 用Green 函数法求解边值问题:()222220,2,,|,.y u u y x x y u x x ϕ=⎧∂∂+=<-∞<<+∞⎪∂∂⎨⎪=-∞<<+∞⎩七、计算题(本题10分)设(1)i μ(1,2,...)i =为1()J x 的正零点,将函数()f x x =()01x <<展开成贝塞尔函数(1)1()i J x μ的级数.。
《计算方法》学期在线作业(一)题目和选项如下所示A:AB:BC:CD:D参考选项:A题目和选项如下所示A:AB:BC:CD:D参考选项:D题目和选项如下A:AB:BC:CD:D参考选项:B。
A:(1/4,1/2,3/4)B:(1/4,1/4,1/4)C:(1/64,1/8,27/64)D:(1/16,1/4,9/16)参考选项:D题目如下A:(5/9,5/9,1/9)B:(5/9,5/9,-1/9)C:(3/9,3/9,3/9)D:(2/3,1/3,0)参考选项:B取等距的7个节点,用复合梯形公式计算得到的近似值为()。
A:1/4B:1/2C:37/72D:65/96参考选项:C迭代算法由初始值开始迭代计算,下列表述中正确的是()。
A:对于所有实数a迭代算法都是稳定的B:对于所有实数a迭代算法都是不稳定的C:对于满足的a对应的迭代算法是稳定的D:对于满足的a对应的迭代算法是不稳定的参考选项:D题目和选项如下所示A:AB:BC:CD:D参考选项:B用抛物线(辛普生)公式计算积分得到的近似值为( )。
A:1/6B:1/2C:1D:3/16参考选项:D。
A:(1/6,4/6,1/6)B:(1/3,1/3,1/3)C:(1,4,1)D:(2,2,2)参考选项:C下列论述中正确的是()。
A:求解线性方程组的克拉姆法则只适用于阶数较小的方程组,对于高阶方程组来说计算量太大B:如果不考虑计算过程中的舍入误差的影响,求解线性方程组的直接法经有限次运算后就能求得方程组的精确解C:求解线性方程组的迭代解法是逐步逼近方程组的精确解,有限次迭代得到的是近似解D:求解大型稀疏线性方程组一般用直接法参考选项:A,B,C误差的来源是多方面的,主要有()。
A:模型误差B:截断误差C:思维误差。
中国石油大学计算机第三次在线作业答案
1.一元多项式的倒数是什么?
答:一元多项式的倒数是倒排一元多项式,使多项式中的每一项的系数都取反。
2.对于一个有穷的二维网格,权值路径的求解方法是什么?
答:权值路径求解方法是使用动态规划技术,通过求解权值最大路径来求解权值路径。
3.如何定义堆栈的抽象数据类型?
答:堆栈的抽象数据类型由两个基本操作组成:入栈和出栈,入栈操作将新数据元素添加到堆栈的顶部,出栈操作则从堆栈的顶部移除数据元素。
4.什么是回溯法?
答:回溯法是一种算法,用于在一堆可能的解决方案中寻找解决问题的最优解。
它尝试一系列的可能解,如果发现当前解不满足约束条件,就返回到前一个可能解,回溯法一般用于解决有限的递归问题。
5.什么是贪心算法?
答:贪心算法是一种在每一步都做出当前最优解的算法,它不会回头重新检查以前的决定,而是优先选择被认为是最优的选择。
贪心算法可以用来解决优化问题,它的做法是在每一步都尝试尽可能做出最优的选择,最终得到最优解。
6.如何定义树的抽象数据类型?
答:树的抽象数据类型由节点和指向分支的链接组成。
中国石油大学《计算机应用基础》复习题一、选择题(题)1.下列各进制数中表示值最大的是()。
、十进制数、八进制数、二进制数、十六进制数2.两个二进制数和相加的结果是()。
、、、、以上都不对3.下列各数中最小的是()。
、十进制数、二进制数C、八进制数、十六进制数1A4.表示种状态的二进制数至少需要()位二进制编码。
、、、、5.以下字符的码值最大的是()。
、、、、6.冯·诺伊曼体系结构的核心设计思想是()。
、存储程序原理、计算机中的数据以二进制表示、计算机硬件由五大部件组成、程序设计7.第一台全数字电子计算机()于年诞生、、、、银河8.以晶体管为部件的计算机是()计算机。
、第代、第代、第代、第代9.计算机的发展阶段通常是按计算机所采用的()来划分的。
、内存容量、电子器件、程序设计语言、操作系统10.计算机按规模分为巨、大、中、小、微型计算机,其发展趋势为()。
、巨型机、大型机、微型机、巨型机和微型机11.利用计算机来模仿人的高级思维活动称为()。
、数据处理、过程控制、计算机辅助设计、人工智能12.利用计算机进行绘制建筑工程图纸属于()。
、数据处理、过程控制、计算机辅助设计、科学计算13.的意思是()、字节、字、二进制位、字长14.在计算机系统中,通常规定一个由()个表示。
、、16 C、、15.计算机中,关于“”的说法,下列说法正确的是()。
、数据最小单位,即二进制数的位、基本存储单位,对应位二进制位、数据最小单位,对应位二进制位、基本运算单位,二进制位数不固定16.微机硬件系统中最核心的部件是()。
、内存储器、输入输出设备、、硬盘17.下列叙述中,属于特点的是()。
、可随机读写数据,且断电后数据不会丢失、可随机读写数据,且断电后数据全部丢失、只能顺序读写数据,且断电后数据不会丢失、只能顺序读写数据,且断电后数据全部丢失18.下列存储器存取速度最快的是()。
、、内存、软盘、光盘19.下列说法正确的是()。
1.计算方法实际计算时,由于受计算机字长限制而导致的误差称为 舍入误差 。
2.x *=1.1021是经过四舍五入得到的近似数,有 5 位有效数字,相对误差限为 0.5*10-4。
3.利用二分法求方程1-x-sinx=0在[0,1]内的根要二分 15 次。
(ε≤0.5*10-4) 4.写出用Newton 法建立求b 的迭代公式 x k+1=(x k 2+b)/2x k 。
5.使用矩阵分解法求解线性方程组时,平方根法适用于 系数矩阵为对称正定矩阵的方程组 ,追赶法适用于 系数矩阵为三对角阵的方程组 。
6.设线性方程组Ax=b ,为⎩⎨⎧=+=+7.07511072121x x x x ,则||A||2= 14.933 ,Cond ∞(A)为289 ,若右端向量有扰动δb=(0.01,-0.01)T,则解的相对误差限为 2.89 。
7.求解数值积分的Simpson 公式的代数精度为: 3 ,若将积分区间n 等分,步长为h, 则复化Simpson 公式的截断误差为h 的几阶无穷小,即 O(h ?4 )8.应用龙贝格求积公式求积分,其整个计算过程的特点是:将积分区间逐次分半,并将每一公式先后两次的计算结果按一定线性组合构成新的精度较高近似值。
9.常微分方程初值问题的数值解法分为单步和多步,显式和隐式,下列方法属于哪一类?龙格-库塔法: 单步、显式 ,阿当姆斯内插公式: 多步、隐式 。
10.若s(x)=⎪⎩⎪⎨⎧≤≤-++≤≤+)21(12)10(2323x cx bx x x x x ,是以0,1,2为节点的三次样条函数,则b=-2 ,c= 3 。
二、解答题(24分,每题6分)1.看书上或课件定义2.对于方程组-1 4 2 2 -3 10 5 2 1x1 x2 x35 9 8试构造一收敛的高斯-赛德尔迭代格式,并说明收敛理由。
解:将方程组变换为:系数矩阵为严格对角占优阵,则方程组存在收敛的高斯-赛德尔迭代格式。
把方程组等价变形为:⎪⎪⎪⎩⎪⎪⎪⎨⎧++-=+-=+--=10921031513453211412583512521x x x x x x x x x 收敛的高斯-赛德尔迭代格式为:⎪⎪⎪⎩⎪⎪⎪⎨⎧++-=+-=+--=++++++10921031513453211412583512521)1()1()1()()1()1()()()1(k k k k k k k k k x x x x x x x x x 3.以线性拟合为例简述最小二乘原理。
答:设近似函数为y=a+bx ,R=∑=-+ni i iy bxa 12)(。
根据极值理论,要使R 达到最小,必有:0)(21=-+=∂∂∑=ni i i y bx a a R, 0)(21=-+=∂∂∑=i ni i i x y bx a b R由方程组可以解出a ,b 的值,从而得到拟和曲线的表达式。
4.确定下列求积公式的常数a ,使其代数精度尽量高,并判定其具有的代数精度。
5 2 1-1 4 2 2 -3 10x1 x2 x38 5 9⎰-++≈hh f f ah h f f hdx x f 02)](')0('[)]()0([2)( 解:当f(x)=1时:⎰+==h hh dx 0]11[21当f(x)=x 时:]0[2]11[]0[221202h h ah h h h xdx h +=-++==⎰当f(x)=x 2时:]20[]0[23120232h ah h h h dx x h -++==⎰,解得:a=1/12当f(x)=x 3时:]30[121]0[241220343h h h h h dx x h -++==⎰当f(x)=x 4时:]40[121]0[251320454h h h h h dx x h -++≠=⎰说明所求求积公式具有三次代数精度。
三、证明题(16分,每题8分)1.若f(x)=(x-x 0)(x-x 1)...(x-x n ),x i 互异,证明当k=n+1时f[x 0,x 1,...,x k ]=1。
证明:由差商性质:∑=+-----=ki k i i i i i i i x x x x x x x x x f 0110))...()()...(()(x k]x 1,...,f[x 0,当k<=n 时))...()()...(()(110k i i i i i i i x x x x x x x x x f ----+-=0))...()()...(())...()()()...((110110=---------+-+-k i i i i i i k i i i i i i i i x x x x x x x x x x x x x x x x x x 当k=n+1时∑+=++-----=11110))...()()...(()(x k]x 1,...,f[x 0,n i n i i i i i i x x x x x x x x xi f= 0 + 1))...(())...((101101=----++++n n n n n n x x x x x x x x2.证明对于牛顿-科特斯求积公式的科特斯系数有10)(=∑=nk n kC。
证明:由牛顿-科特斯求积公式:∑⎰⎰=+++-=nk ban k n kbadx x n f x f Ca b dx x f 0)1()()()1()()()()(ωξ!设f(x)=1则⎰++ban dx x n f )()1()()1(ωξ!=0。
所以:∑⎰=-=-=nk k n k bax f C a b a b dx 0)()()(1,即:1)(0)(=∑=nk k n kx f C四、计算题(26分)1.(10分)给出sinx 在[0.4,0.7]的数值表如果使用二次插值求sin0.63891的近似值,问如何选取结点,才使其近似值的误差较小?并求该近似值,小数点后保留5位数字。
(注意:拉格朗日插值与牛顿插值两种方法任选,若采用牛顿插值,构造出差商表)解:应选三个节点,使截断误差|R 2(x)|<=|f (3)(ξ)||(x-x0)(x-x1)(x-x2)|尽量小。
故最靠近0.63891的三个节点一定满足要求。
显然,取{0.5,0.6,0.7}。
(1)采用拉格朗日插值:L 2(x) = 22 0.644)6.07.0)(5.07.0()6.0)(5.0(640.564)7.06.0)(5.06.0()7.0)(5.0(43 0.479)7.05.0)(6.05.0()7.0)(6.0(⨯----+⨯----+⨯----x x x x x x= 220.64402.0)6.0)(5.0(640.56401.0)7.0)(5.0(43 0.47902.0)7.0)(6.0(⨯--+⨯---⨯--x x x x x x所以:sin0.63891 ≈ L 2(0.63891)=220.64402.0)6.00.63891)(5.00.63891(640.56401.0)7.00.63891)(5.00.63891(43 0.47902.0)7.00.63891)(6.00.63891(⨯--+⨯---⨯--=220.64402.00.038910.13891640.56401.0)06109.0(0.1389143 0.47902.0)06109.0(0.03891⨯⨯+⨯-⨯-⨯-⨯=22 0.64402.0054000.64 0.56401.000849.043 0.47902.000238.0⨯+⨯+⨯-=17394.047938.005705.0++-=0.59627(2)采用牛顿差值:N 2(x) = 0.479 43 + 0.8521(x-0.5) - 0.2815(x-0.5)(x-0.6) 所以sin0.63891 ≈ N 2(0.63891)= 0.479 43 + 0.8521*(0.63891-0.5) - 0.2815*(0.63891-0.5)*( 0.63891-0.6) =0.479 43 + 0.8521*0.13891 - 0.2815*0.13891*0.03891 =0.479 43 + 0.11837 - 0.00152 =0.596282.(8分)设max|f ’’(x)|<=81,x ∈[2,8],用复化梯形公式计算⎰82)(dx x f 的近似值时,为使截断误差的绝对值不超过51021-⨯,至少应将[2,8]分为多少等份?解:用复化梯形公式,截断误差:R n (f) = )(''112)28()(''12232ηηf nf h a b ⨯--=⨯-- 因为max|f ’’(x)|<=81所以| R n (f) |<=5231021811126-⨯<=⨯⨯=n 解得n>=671所以至少分为671等份。
3.(8分)用欧拉预报-校正法求初值问题⎩⎨⎧=+=0)0(1'2y y y 在x=0.3,0.6处的数值解,步长h=0.3,小数点后保留5位数字。
解:由预报-校正公式有:⎪⎩⎪⎨⎧++++=++=+++])(11[2)1(20121201n n n n n n ny y h y y y h y y h=0.3,n=0,1,2,... 利用上述公式,及y(0)=0得:⎪⎩⎪⎨⎧=++++==++=3135.0]3.0101[*23.003.0)01(*3.002101y yy(0.3)≈y 1=0.3138⎪⎩⎪⎨⎧=++++==++=69026.0]64298.013135.01[*23.03135.064298.0)3135.01(*3.03135.0221202y yy(0.6) ≈y 2=0.69026一.填空k1.已知π=3.1415926…若其近似值的绝对误差限为0.5×10-5,则该近似值是什么?2、对于充分接近90度的x, 为不损失有效数字,应对公式1- sin(x) 做何变化?3、对于不动点迭代X k+1=Φ(X k ) , 若在不动点x*满足Φ‘(x*)≠0,则该迭代格式是几阶收敛的4、牛顿迭代法的特点是什么 ?对于单根,它是几阶收敛的?5、关于线形方程组系数矩阵的条件数 a 、 反映绝对误差放大倍数 b 、 反映相对误差放大倍数c 、 条件数越大,方程组越呈“良”态6、写出两种非线形方程的解法7、追赶法适合解系数矩阵为 的方程组8、设xi (i=0,1,2,3,4)为互异结点 ,li(x)为对应的插值基函数 则:∑=43)(i x li xi = ∑=++42)()24(i x li xi xi=9、什么是三次样条插值函数?,写出三个要点10、A= 1 a ,当a= ,A可做LLT分解,1 2其中L的元素满足L=11、向量X=(x1,x2,x3)T , 则 | x1+2x2|+| x1+x3| 是不是一种向量范数?二.解答:1、当A有扰动δA和b有扰动δb时,如何用矩阵A的条件数去估计方程组的相对误差||δx|| / ||x||?2.写出gauss列主元的算法描述三、解方程组已知方程组 Ax=b , 其中A= 1 2 b= 10.3 1 2(1)写出解此方程组的Jacobi迭代公式,讨论用Jacobi迭代解此方程组的收敛性(2)写出解此方程组的Gauss-Seidel迭代公式,讨论用Gauss-Seidel迭代解此方程组的收敛性四.求形如 y=ae bx ( a, b 为常数,且a>0 ) 的经验公式,使它能和下表数据相拟合:已知对数表五、已知函数表:1、构造差商表,写出Newton插值多项式2、写出Laglanre插值多项式3、写出该插值多项式的余项六、设 f (x) =g(x)h(x)证明: f [ x0 , x1 ] = g(x0) h[x0 , x1] + g [x0 ,x1] h(x1)七、用最小二乘法解矛盾方程组2x + 3y = 6x + y = 22x + y = 42.补充Newton迭代的大范围收敛性定理,并完成所给问题(8分)(1)Newton迭代收敛性定理如下:设f(x)在区间[a, b]上二阶导数存在,且对于x ∈[a,b]满足:①②③④则Newton迭代法收敛于f(x) =0在[ a, b]上的唯一根。