设[tex=7.071x1.286]Lu8HIcpZ6kO7EKB5TUbh2uCJdghAM1sLin7pONsDKz4=[/tex]。（1）写出解[tex=3.714x1.286]0ZoDYEiHpPjb6Gw3Oeomrg==[/tex]的Newton迭代格式。（2）证明此迭代格式是线性收敛的。
举一反三
- 用迭代法求解下述线性方程组:[tex=10.786x3.929]7EJHVCtO2IWq3KpdB+jQsnkb7DW+/SpRiPSBe5KwiaaxWfR5Lfq+Hi077Ucj0weF+ETXx9iu3nod7pl1UtUTry1YLTMg4D3Q/7VqU783aaYzA01CIa3Go0XgfmE1s8OUKLm/vzBGUf65MosN7Vb/fPAtPy5Uvea+4g7U8ByYs+7lD0v8XexZLXJbRj2PcLWS[/tex](1)分别写出雅可比迭代、GS迭代、SOR迭代([tex=3.214x1.0]MFgkChukcohooa6iaLcR2w==[/tex]) 的迭代格式；(2) 判断上述三个迭代格式的收敘性, 并说明理由；(3) 用收敛的迭代格式分别计算方程组的解，要求满足[tex=11.786x2.357]3kRqjnXEHaOzBR9r8vWb96A+vNOgwLg56qvrp/8CcyYDvY5AywTfd/xCUxv2vjti2Sjf944sZSG71Eobmf77uMVDntSSsxV01gIHTc+vDUM=[/tex].
- 试写出求方程[tex=3.5x2.357]c8V8BtPHWI/+h3aP5LkaZw==[/tex](其中c为已知正常数)的Newton迭代格式，并证明当初值[tex=0.929x1.0]XQ8c0totc8uufRPOvpPxwQ==[/tex]满足[tex=4.857x2.357]hGdSLCjIEVGi3Pyiy+k7jShfhAX5Zmg5+FVDIT0ecRg=[/tex]时迭代格式收敛。该迭代格式中是否含有除法运算?
- set1 = {x for x in range(10)} print(set1) 以上代码的运行结果为？ A: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} B: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9,10} C: {1, 2, 3, 4, 5, 6, 7, 8, 9} D: {1, 2, 3, 4, 5, 6, 7, 8, 9,10}
- 给定线性方程组 [tex=16.5x3.929]NeoTBlf1CmkUoMf07Si5dAGux5rN26LAYw4E11YkLsNiQeEaZIfEM3bk2Epo7fpPytYUEKsMESQSOATG1CRA02xzjBvxaGFLTHV6h2D5mTijnBOHmwFWUE9rpKanyf/gKkrxkWGpVtqOGZY9TiY6rJLAWJMwwkwGk2xU1eZwIy+LgVrCy6qubcpGGN4xAl7vGNCtfTgE2rnzPYeZO8L/X80JC2uyzK60ozLKLnoKP0Eln6M4v5h78nl+ird8KpGLhA/Mld+dthdHfjtoTUuJVg==[/tex].1)写出雅可比迭代格式和高斯-赛德尔迭代格式；2)证明雅可比迭代法收敛而高斯赛德尔迭代法发散；3)给 [tex=5.929x1.571]4wpeG2iubwhDqS5afdX5xPkhtj/JG/6dEzctIAjN3UQ=[/tex]，用迭代法求出该方程组的解，精确到[tex=11.643x2.357]sbrfngj8hJee1HYCnwltAUhnyXBvvjLEGtCBzkdJiKOKmVIReuPa++FqYMyPUva7pJsXNLcC4bfcYUhtn7FZx9ysZvMJnLkbYVOd8XMawVc=[/tex].
- 写出求解方程[tex=6.357x2.357]zKUh1fkEfgcGsE+/+kHKJ9iZRtFZsQiDpBDffeRC7zI=[/tex]的Newton迭代格式并判断以下情形的收敛性。（1）[tex=2.786x1.214]u1CAhHqf6iuer+xzQnhMnA==[/tex]或[tex=2.786x1.214]rrZPRV7TTHm1hu8oo8kdWg==[/tex]；（2）[tex=2.214x1.214]LJXdFaUr90iYpUVNdMvX/A==[/tex]或[tex=2.214x1.214]ToesHW4GTsD+l3fRVL4fig==[/tex]；（3）[tex=4.643x1.214]j4VMGks5lFWq/6MEikHz4g==[/tex]。