设 [tex=3.643x1.5]wQVUWZnb5HIcHy0u2nadlg==[/tex], 求 [tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex]在区间[tex=2.0x1.357]AUoDsQBgen8/+sL3yGoyYA==[/tex] 上的分段三次 Hermite 插值函数[tex=2.571x1.357]kngO/2HcGZGPfSQUQY6mDg==[/tex] 并估计误差, 取等距节点且 [tex=3.643x1.357]/1LfbGBc+yIBmbupqXh60w==[/tex]

2022-07-23

设 [tex=3.643x1.5]wQVUWZnb5HIcHy0u2nadlg==[/tex], 求 [tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex]在区间[tex=2.0x1.357]AUoDsQBgen8/+sL3yGoyYA==[/tex] 上的分段三次 Hermite 插值函数[tex=2.571x1.357]kngO/2HcGZGPfSQUQY6mDg==[/tex] 并估计误差, 取等距节点且 [tex=3.643x1.357]/1LfbGBc+yIBmbupqXh60w==[/tex]

答案：

解 [tex=18.429x1.357]wAKL++LDWeA2KPlw1xfrx4vymWilTG3GzchWslUAcAniB71BGuNsQ6p2n00rcxadOcXWrySip5BMyPGde/agVQ==[/tex][tex=13.643x1.357]tnK7XiVsIato7RrW2biaSeHeQkC63VeOzibNKefTV5nilWtKSpA4uQk1RmzYhOlZ9nc4lrqa2NrixGpsnH0dcj1xvn37V1r0Fvb2cUD5Ots=[/tex], 有[tex=21.643x4.571]GzKSwnLSXriIv3H2H+7vbbQ1kRYSbkn+odctuDP8CWed6FBLXWkgN9Z1mYRzBB3mxIK7D/GENtqQKAgLMUMVSGD0zkVqVpd7sp8xrj96jf1xgot3HRBYTm7TkIQcOhIgcyTgl0WgRhHChES7ftvN1ZxvGDpvZdqoIqLrHSCSpexP+OraPeCdMqlUDlPh41yy9Qd5y8k4If1R2I1mKhK6XuhTGE1GKn9qFBWj652f9qLQCcwrJS2JSrveCSfL6rc1GtdSKiLmq68n25Fk79/PfxN65dLxCfAgeXzMCMyW8YvrLpaRiJWx4tHy9ZVufbu83R8TfpepYpiYHU4l4rKK4p99tB1vSAq4XAUfPZ3SoAc=[/tex][tex=26.857x8.5]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[/tex]

举一反三

内容

0
已知[tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex]是以2为周期的周期函数，且在[tex=2.0x1.357]BKlvvhPbvHmrH3NqEoQqGQ==[/tex]上有[tex=3.643x1.5]/C1UNKhjcg4SoGLfWhelmw==[/tex]，求[tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex]在[tex=2.0x1.357]S9Knzv0BvymT1xFCEVwi7w==[/tex]上的表达式.
1
设 [tex=7.857x1.571]YPqHFuAahknf9AbHQjYMYvwG2Z4uR4XHF1WwqETF1CI=[/tex] 在 [tex=5.071x1.143]WbFHLHyJoSkbfDEfXR/tLcVjcSyr2pX9QdzN43wf6xQ=[/tex] 上取 [tex=2.714x1.214]+/r48fIEUYRtkCIw7Xyzkg==[/tex] 按等距节点求分段线性插值函数[tex=2.5x1.357]stiH941sUDFRKJvghdJAmQ==[/tex]计算各节点间中点处的[tex=2.214x1.357]F553BFjbBQ55xruo9OuGQA==[/tex]与 [tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex] 的值,并估计误差.
2
设 [tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex]在 [tex=2.0x1.357]AUoDsQBgen8/+sL3yGoyYA==[/tex] 上连续,且[tex=6.0x2.786]388S0HIqirGk5XoWsuogsDXJkocYmuT8+v2HFbn6jok=[/tex], 证明 : 存在 [tex=3.357x1.357]BsjbQo5VxYXTRwty7i/6ug==[/tex], 使得[p=align:center][tex=6.857x1.357]XY7JC6DRxDlBumWPQU62gnZ5AhHjWw1CSZfJzRrMLFM=[/tex]
3
对函数[tex=2.214x2.357]Hqxa/UCqq6/+StWVpW6nUr/ywv3F3oCfiNclBLHvryo=[/tex] , 在区间[tex=2.0x1.357]AUoDsQBgen8/+sL3yGoyYA==[/tex]上用等距线性插值、等距[tex=3.857x1.0]aSjk4o7nmJkfQs7mJKmLIA==[/tex]3 次插值、等距样条插值，问步长[tex=0.643x1.0]uPu/UBwxTDghY6MHYDLmcA==[/tex]应取多少才能保证各自的截断误差小于[tex=2.0x1.214]FpeOfmuZawZqwM2eXSPGDw==[/tex] ?
4
设[tex=0.786x1.0]I/kNMtd8YcgkWCrgriW/hA==[/tex]是[tex=2.0x1.357]AUoDsQBgen8/+sL3yGoyYA==[/tex]中的不可测集，令[tex=11.929x3.071]0Oc6OdDyTxw5ASPscCgHyWfU1471GKC1BYEnY7gvGnIeyTHPIIbXnMwHjWvcn9Azl/rA7hoIDTdEZ/xP6nglRc4EjMbxHStwwUjhgC2ak8wa+YtzC2kNDdAo2ZeNs3cJ[/tex]问 [tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex]在 [tex=2.0x1.357]AUoDsQBgen8/+sL3yGoyYA==[/tex]上是否可测 ?[tex=2.429x1.357]HahJs8lvA4tV0CFg1fYnxw==[/tex]是否可测?