1. 牛顿法与弦截法的收敛性不受初值的影响 ( )

  2. 答案:错
  3. Adam方法是所有ai除了a0=1外其余全为0的多步法。( )

  4. 答案:对
  5. 柯特斯系数是不依赖与积分区间[a,b]以及被积函数f(x)的常数,只要给出插值点数n,就可以求出柯特斯系数。( )

  6. 答案:对
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  8. 答案:错
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  10. 答案:对
  11. 数值计算的稳定性是指每一步数值计算产生的误差不至于影响到以后的计算。( )

  12. 答案:对
  13. n阶的牛顿—柯特斯求积公式是对于任何不高于n次的多项式准确成立的。( )

  14. 答案:对

  15. 答案:错

  16. 答案:对

  17. 答案:对
  18. 多步法是指yn+1用yn、yn-1…和f(xn+1,yn+1)、f(xn,yn)、f(xn-1,yn-1)…来表达,即用到前面多步的数据。( )

  19. 答案:对
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  21. 梯形法在求yn+1时,用xn、xn+1两点导数平均值作为近似斜率,因此不是单步法。( )
  22. 对于n+1个互异的节点,若f(x)为不高于n次的多项式,则f(x)关于这组节点的n次插值多项式就是他自己。( )
  23. 数值计算方法的计算对象是( )
  24. 下列公式哪些属于牛顿—柯特斯公式?( )
  25. 对于f(x)=x3+x+1,( )。
  26. 计算方法关注的误差主要是( )。
  27. 设向量x=(2,-4,6)’,则x向量的无穷范数为( )。
  28. 已知x=[1,2,3],y=[-1,2,1],则过这三点的二次插值多项式中x2的系数为( )。
  29. 已知近似值a=138.00的绝对误差限为0.005,则它有几位有效数字?( )。
  30. 求解方程lnx-x+2=0的根的Newton迭代公式为( )。
  31. 插值与拟合不同的是( )。
  32. 已知x=[-2,-1,0,1,2],y=[0,1,2,1,0],用y=c0+c1x+c2x2拟合,则( )。
  33. 二阶龙格-库塔法需要满足 λp=_____。( )
  34. 求解方程lnx-x+2=0的根的弦截法迭代公式为( )
  35. 已知e=2.71828...,则近似值a=2.718的相对误差界为 ?( )。
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  37. 设f(x)在其零点x∗邻近二阶可微,且f'(x∗)≠0,当初值在根附近选取时,Newton法至少是( )
  38. 隐式Adam法是令____________。( )
  39. 已知x=[-3,-2,-1,2,4],y=[14.3,8.3,4.7,8.3,22.7],lny=[2.6607,2.11626,1.54756,2.11626,3.12236],用最小二乘法求形如y=aebx的经验公式( )。
  40. 下列关于三次样本插值与一般3次多项式插值陈述准确的是( )。
  41. 3.142和3.141分别作为π的近似数具有几位有效数字?( )。
  42. 已知x=[1,2,3,4],y=[12,15,17,21],则其三阶差商为( )。
  43. 牛顿差分表的口诀是( )。
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  45. 有n个互异节点与其函数值,得到的拉格朗日插值基函数次数为( )。
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  47. 已知x=[0,0.5,1,1.5,2,2.5],y=[-2,-1.75,-1,0.25,2,4.25]所确定的插值多项式的次数是( )。
  48. 插值与拟合主要适用以下哪类问题( )。
  49. 下列哪一项不是利用积分中值定理推导出的积分方法?( )
  50. 当n>=( )时,柯特斯系数有正有负。
  51. [removed]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  53. 梯形法是____阶精度、____式的。( )
  54. 三阶R-K法的斜率线性组合为___k1+___k2+___k3。( )
  55. 隐式法的绝对稳定区域要比显示法大。( )
  56. 任何实用的数值算法都必须满足以下的标准:( )
  57. [removed]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
  58. n=4时,柯特斯系数为( )。
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  60. 下列哪些情况下可以用数值的方法求函数的导数值?( )
  61. 使用高阶复合求积公式求解定积分,若已知区间上7个等分结点的函数值,用复合辛普生公式,区间等分数为?( )
  62. [removed]iVBORw0KGgoAAAANSUhEUgAAAC4AAAAiCAYAAAAge+tMAAABOklEQVRYCe2WjQ6DMAiE+/4v7YLJmRvyU6cd1mjSlMFRviJb1pZJnzYp93IYvLW2yKp+fiJ4wU+8trDj3ljcuuMeHC7jxU808VCq2/FqsOwWzwLHOGS3roybHb/7mEjDXvB/j83QjmPksu9MFreaMhR8ncWO/zW4oAXo+S4FtzoXQUFvadjHNi5yGTgO511sLBSUXfuQwzH4sHP+qtMOJFt+z8eHs31WH511ScelAJYHy34GYps1YocxLc4SMn1UDLmsYRtxMHixNc5i2FECNLyLHov9ng2t3kUPH9vi08/ek7wifUDV5+eA86uq6mZP3V3HpwbvuXG1xux4NVRP/RQco2P9JPUUGKUJwRmW7VEwR87dwNFZTmZYtllTZX+BawiGZVvrKj5v4F5xAb4btLCm4N6Fqv3Tgn8A1IsTMfxBtVEAAAAASUVORK5CYII=
  63. 同一个问题中,需要将一个拟合函数的残差平方和与其他拟合函数残差平方和比较才能判断优劣。( )
  64. 已知x=[2,4,6,8]对应y=[2,11,28,40],使用最小二乘法求拟合多项式为( )
  65. 以下陈述正确的是( )。
  66. 分段线性插值的误差一般不等于拉格朗日插值的误差。( )
  67. 求4中拟合多项式的残差平方和( )
  68. 已知f(4)=2,f(9)=3,则f(x)的线性插值多项式为( )。
  69. 同一问题中,可以用多种函数拟合出不同的拟合曲线。( )
  70. 高斯消去法属于线性方程组数值解法中的迭代法。( )
  71. 用简单迭代法求方程f(x)=0的实根,把方程f(x)=0表示成x=g(x),则f(x)=0的根是( )
  72. 非线性方程的求根方法中,正割法收敛速度比Newton迭代法快。( )
  73. 如果迭代格式在根的附近导数值的模大于1,则迭代发散。( )
  74. 若x*是f(x)=0的重根,则牛顿不收敛。( )
  75. 以下对非线性方程的求根方法中哪些是线性收敛的?( )
  76. 若f(a)f(b)<0 ,则f(x)在(a,b)内一定有根。( )
  77. 两近似值之商的相对误差等于被除数的相对误差与除数的相对误差之差。( )
  78. 相对误差是个无名数,没有量纲。( )
  79. 计算机进行乘除运算时按照先舍入后运算的原则。( )
  80. 工科人认知世界的时候,需要认可误差的存在。
  81. 求解高阶线性方程组(比如,大于150阶),用克莱姆法则来直接求解也是可以接受的。
  82. 计算方法是一门理论数学课,可以获得寻求数学问题的精确解析解的知识
  83. 不需要掌握很多很好的计算方法,单单凭借计算机强大的能力就可以解决大部分实际问题。
  84. 解决某些实际问题时,选择不合适的计算方法有可能无法得到满意的结果。
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