計(jì)算方法試題集及答案(新)

1、11.為精確值的近似值；為一元函數(shù)的近似值；xx??xfy???xfy?1為二元函數(shù)的近似值，請(qǐng)寫(xiě)出下面的公式：：??yxfy???yxfy2?exx??rxxex????????1yfxx????????????1rrxfxyxfx??????????????2fxyfxyyxyxy?????????????????????222rfxyexfxyeyyxyyy?????????2、計(jì)算方法實(shí)際計(jì)算時(shí)，對(duì)數(shù)據(jù)只能取有限位表示，這時(shí)所產(chǎn)

2、生的誤差叫舍入誤差。3、分別用2.718281，2.718282作數(shù)e的近似值，則其有效數(shù)字分別有6位和7位；又?。ㄈ挥行?shù)字），則。31.73?2131.73102???4、設(shè)均具有3位有效數(shù)字，則的相對(duì)誤差限為0.0055。121.2163.654xx??12xx5、設(shè)均具有3位有效數(shù)字，則的誤差限為0.01。121.2163.654xx??12xx?6、已知近似值是由真值經(jīng)四舍五入得到則相對(duì)誤差限為0.0000204.2.456

3、0Ax?Tx7、遞推公式如果取作計(jì)算則計(jì)算到時(shí)誤差為?????0nn1y=2y=10y1n=12?021.41y??10y這個(gè)計(jì)算公式數(shù)值穩(wěn)定不穩(wěn)定不穩(wěn)定.81102?8、精確值，則近似值和分別有3位和?14159265.3??141.31??1415.32??4位有效數(shù)字。9、若則x有6位有效數(shù)字，其絕對(duì)誤差限為12105。2.71828xex???10、設(shè)x的相對(duì)誤差為2％，求(x)n的相對(duì)誤差0.02n11、近似值0.231x?關(guān)

4、于真值229.0?x有(2)位有效數(shù)字；12、計(jì)算方法主要研究(截?cái)?誤差和(舍入)誤差；3??????????????=VVVVLWHLWHWHLHLWLWH??????????????????相對(duì)誤差可估計(jì)為：????rVVV???而已知該水池的長(zhǎng)、寬和高的數(shù)據(jù)的絕對(duì)誤差滿足??????0.010.010.01LWH??????故求得該水池容積的絕對(duì)誤差限和相對(duì)誤差限分別為????????????325200.0150200.015

5、0250.0127.5027.501.11025000rVWHLHLWLWHVVV?????????????????2.已知測(cè)量某長(zhǎng)方形場(chǎng)地的長(zhǎng)a=110米寬b=80米.若????0.10.1aabb????米，米試求其面積的絕對(duì)誤差限和相對(duì)誤差限.解：設(shè)長(zhǎng)方形的面積為s=ab當(dāng)a=110b=80時(shí)，有s==11080=8800(米2)此時(shí)，該近似值的絕對(duì)誤差可估計(jì)為??????????=bsssababaab????????????相