电大计算方法试题参考小抄参考

专业好文档计算方法试题参考一计算及推导（5*8）1已知，试确定近似的有效数字位数。2有效数，试确定的相对误差限。3已知，试计算差商4给出拟合三点和的直线方程。5推导中矩形求积公式6试证明插值型求积公式的代数精确度至少是n次。7已知非线性方程在区间内有一实根，试写出该实根的牛顿迭代公式。8用三角分解法求解线性方程组二给出下列函数值表0.40.50.60.70.80.389420.479430.564640.644220.71736要用二次插值多项式计算的近似值，试选择合适的插值节点进行计算，并说明所选用节点依据。（保留5位有效数字）（12分）三 已知方程在内有一实根（1）给出求该实根的一个迭代公式，试之对任意的初始近似迭代法都收敛，并证明其收敛性。（2）试用构造的迭代公式计算的近似值，要求。四 设有方程组（1） 当参数a满足什么条件时，雅可比方法对任意的初始向量都收敛。（2） 写出与雅可比方法对应的高斯赛德尔迭代公式。（12分）五用欧拉预估校正法求解初值问题取h=0.1，小数点后保留5位。（8分）六证明求解初值问题 的如下单步法是二阶方法。（10分）七试证明复化梯形求积公式对任意多的积分节点数n+1,该公式都是数值稳定的。（6分）2003-2004第一学期一填空（3*5）1近似数关于真值有-位有效数字。2的相对误差为的相对误差的-倍。3设可微，求根的牛顿迭代公式-。4插值型求积公式的代数精确度至少是-次。5拟合三点和的常函数是-。二已知有如下的数据12324123试写出满足插值条件以及的插值多项式，并写出误差的表达形式。三（1）用复化辛浦森公式计算为了使所得的近似值有6位有效数字，问需要被积函数在多少个点上的函数值？ （2）取7个等距节点（包括端点）用复化辛浦森公式计算，小数点后至少保留4位。四曲线与在点（0.7，0.3）附近有一个交点，试用牛顿迭代公式计算的近似值，要求五 用雅可比方法解方程组是否对任意的初始向量都收敛，为什么？取，求出解向量的近似向量，要求满足。六用校正一次的欧拉预估校正格式求解初值问题的解函数在处的近似值，要求写出计算格式。（步长,小数点后保留5位有效数字）七设有求解初值问题的如下格式如假设问常数为多少时使得该格式为二阶格式？ 2005-2006第二学期一填空（3*5）1 设近似数都是四舍五入得到的，则相对误差-。2 矛盾方程组的最小二乘解为-。3 近似数关于真值有几位有效数字4 取，迭代过程是否稳定？5 求积公式有几次的代数精确度？二 取初值，用牛顿迭代法求的近似值，要求先论证收敛性。当时停止迭代。三用最小二乘法确定中的常数a和b，使该曲线拟合于下面的四个点（1，1.01）（2，7.04）（3，17.67）（4，31.74）（计算结果保留到小数点后4位）四用乘幂法求矩阵A的按模最大的特征值的第k次近似值及相应的特征向量，要求取初值且这里 A=五考察用高斯赛德尔迭代法解方程组收敛性，并取，求近似解，使得（i=1，2，3）六已知单调连续函数的如下数据用插值法求方程在区间（0.00，1.80）内根的近似值。（小数点后至少保留4位）七设有积分 取5个等距节点（包括端点），列出被积函数在这些节点上的函数值表（小数点后至少保留4位）用复化的simpson公式求该积分的近似值，并且由截断误差公式估计误差大小。八给定初值问题写出Euler预估校正格式取步长为0.2，计算在1.4处的函数的近似值。九设矩阵A对称正定，考虑迭代格式对任意的初始向量是否收敛到的解，为什么？ 计算方法2006-2007第二学期1 填空1）. 近似数关于真值有_为有效数字。2） 适当选择求积节点和系数，则求积公式的代数精确度最高可以达到_次.3） 设近似数，都是四舍五入得到的，则相对误差 的相对误差限_4) 近似值的相对误差为的_ 倍。5） 拟合三点A(0,1), B(1,3)，C(2,2)的平行于轴的直线方程为_.2. 用迭代法求方程在（-1，0）内的重根的近似值。要求1）说明所用的方法为什么收敛；2）误差小于时迭代结束。3用最小二乘法确定中的和，使得该函数曲线拟合于下面四个点 (1.0,1.01), (1.5,2.45), (2.0,4.35), (2.5,6.71) (计算结果保留到小数点后4位)4 设函数有二阶连续导数，在一些点上的值如下1.01.11.20.010.110.24写出中心差分表示的二阶三点微分公式，并由此计算。5 已知五阶连续可导函数的如下数据0101010试求满足插值条件的四次多项式6 设有如下的常微分方程初值问题1） 写出每步用欧拉法预估，用梯形法进行一次校正的计算格式。2） 取步长0.2用上述格式求解。7 设有积分1）取7个等距节点（包括端点），列出被积函数在这些点出的值（保留到小数点后4位）2）用复化simpson公式求该积分的近似值。8 用LU分解法求解线性代数方程组9 当常数c取合适的值时，两条抛物线 与就在某点相切，试取出试点，用牛顿迭代法求切点横坐标。误差小于时迭代结束。参考答案； 1: (1)2, (2) 2n-1 (3) 2.1457*10E-3 （4）1/5 (5) x=12 解：将方程变形为 即求在（-1，0）内的根的近似值牛顿迭代格式为 收敛性证明； 局部收敛定理结果 。3 用最小二乘法 正则方程组为解得 a=1.0072; b=0.45634解 推导中心差分格式得到5 解 截断误差 6 7 0.68058 （0 1 0 1）9 解 两条曲线求导 和切点横坐标一定满足=将等式变形为 牛顿迭代法 结果为 0.34781Winger Tuivasa-Sheck, who scored two tries in the Kiwis 20-18 semi-final win over England, 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 Charnleys effort in their first pool match against England on the opening day.Aussie winger Jarryd Hayne is the competitions 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 interest 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.Id give every award back in a heartbeat just to get across the line this weekend, said Williams.The (lack of) air up there Watch mCayman Islands-based Webb, the head of Fifas anti-racism taskforce, is in London for the Football Associations 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.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 Toures 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 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/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 feet ( Then, I would assume, 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 here - the last try they conceded was scored by Englands 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 that wins you tough, even contests - strong defence, especially on their own goal-line, completing sets and a good kick-chase. Theyve 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 priceless asset going into Saturday.The Kiwis are a lot less experienced but winning a dramatic match like their semi-final against England will do wonders for their confidence.They defeated Australia in the Four Nations final in 2010 and the last World Cup, and know they can rise to the big occasion.