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重排法求解方程 x=g(x) [不动点迭代]

重排法求解方程 x=g(x) [不动点迭代]
几何画板及绘图内容加载中，请稍等……
2013-06-19 19:54
函数微积分导数最值优化函数图像
所属专题 A Level: Numerical Methods for Solving Equations
本范例演示了通过重排方程 f(x)=0 为 x=g(x) 并进行迭代 x_{n+1}=g(x_n) 来寻找方程根的数值方法。①该范例通过可视化展示不动点迭代过程，直观呈现迭代序列的收敛性；②涉及的核心数学概念包括不动点、迭代序列、收敛性以及函数图像；③作图要点使用了 Point, Derivative, Text, Textfield, Segment 等GeoGebra命令，关键对象包括函数f及其导数f'、迭代点posX, posY、缩放参数zoomX, zoomY等；④适合高中及以上数学学习者，用于理解数值方法在方程求解中的应用。

GeoGebra 命令及参数

  1. Point(xAxis) → x_0
  2. Derivative(f) → f'
  3. Text("x_0=", A) → F1
  4. Textfield(f) → inputBox1
  5. Text("x_" * B11 + "_" * A11 * "=", (x(A), y(A) - (B11 * 10 + A11) * 0.15 * zoomY)) → F11
  6. Text("x_" * B12 + "_" * A12 * "=", (x(A), y(A) - (B12 * 10 + A12) * 0.15 * zoomY)) → F12
  7. Text("x_" * B13 + "_" * A13 * "=", (x(A), y(A) - (B13 * 10 + A13) * 0.15 * zoomY)) → F13
  8. Text("x_" * B14 + "_" * A14 * "=", (x(A), y(A) - (B14 * 10 + A14) * 0.15 * zoomY)) → F14
  9. Text("x_" * B15 + "_" * A15 * "=", (x(A), y(A) - (B15 * 10 + A15) * 0.15 * zoomY)) → F15
  10. Text("x_" * B16 + "_" * A16 * "=", (x(A), y(A) - (B16 * 10 + A16) * 0.15 * zoomY)) → F16
  11. Text("x_" * B17 + "_" * A17 * "=", (x(A), y(A) - (B17 * 10 + A17) * 0.15 * zoomY)) → F17
  12. Text("x_" * B18 + "_" * A18 * "=", (x(A), y(A) - (B18 * 10 + A18) * 0.15 * zoomY)) → F18
  13. Text("x_" * B19 + "_" * A19 * "=", (x(A), y(A) - (B19 * 10 + A19) * 0.15 * zoomY)) → F19
  14. Text("x_" * B20 + "_" * A20 * "=", (x(A), y(A) - (B20 * 10 + A20) * 0.15 * zoomY)) → F20
  15. Text("x_" * B21 + "_" * A21 * "=", (x(A), y(A) - (B21 * 10 + A21) * 0.15 * zoomY)) → F21
  16. Text("x_" * B22 + "_" * A22 * "=", (x(A), y(A) - (B22 * 10 + A22) * 0.15 * zoomY)) → F22
  17. Text("x_" * B23 + "_" * A23 * "=", (x(A), y(A) - (B23 * 10 + A23) * 0.15 * zoomY)) → F23
  18. Text("x_" * B24 + "_" * A24 * "=", (x(A), y(A) - (B24 * 10 + A24) * 0.15 * zoomY)) → F24
  19. Text("x_" * B25 + "_" * A25 * "=", (x(A), y(A) - (B25 * 10 + A25) * 0.15 * zoomY)) → F25
  20. Text("x_" * B26 + "_" * A26 * "=", (x(A), y(A) - (B26 * 10 + A26) * 0.15 * zoomY)) → F26
  21. Text(C11, (x(A) + 0.4 * zoomX, y(A) - (B11 * 10 + A11) * 0.15 * zoomY)) → G11
  22. Text(C12, (x(A) + 0.4 * zoomX, y(A) - (B12 * 10 + A12) * 0.15 * zoomY)) → G12
  23. Text(C13, (x(A) + 0.4 * zoomX, y(A) - (B13 * 10 + A13) * 0.15 * zoomY)) → G13
  24. Text(C14, (x(A) + 0.4 * zoomX, y(A) - (B14 * 10 + A14) * 0.15 * zoomY)) → G14
  25. Text(C15, (x(A) + 0.4 * zoomX, y(A) - (B15 * 10 + A15) * 0.15 * zoomY)) → G15
  26. Text(C16, (x(A) + 0.4 * zoomX, y(A) - (B16 * 10 + A16) * 0.15 * zoomY)) → G16
  27. Text(C17, (x(A) + 0.4 * zoomX, y(A) - (B17 * 10 + A17) * 0.15 * zoomY)) → G17
  28. Text(C18, (x(A) + 0.4 * zoomX, y(A) - (B18 * 10 + A18) * 0.15 * zoomY)) → G18
  29. Text(C19, (x(A) + 0.4 * zoomX, y(A) - (B19 * 10 + A19) * 0.15 * zoomY)) → G19
  30. Text(C20, (x(A) + 0.4 * zoomX, y(A) - (B20 * 10 + A20) * 0.15 * zoomY)) → G20
  31. Text(C21, (x(A) + 0.4 * zoomX, y(A) - (B21 * 10 + A21) * 0.15 * zoomY)) → G21
  32. Text(C22, (x(A) + 0.4 * zoomX, y(A) - (B22 * 10 + A22) * 0.15 * zoomY)) → G22
  33. Text(C23, (x(A) + 0.4 * zoomX, y(A) - (B23 * 10 + A23) * 0.15 * zoomY)) → G23
  34. Text(C24, (x(A) + 0.4 * zoomX, y(A) - (B24 * 10 + A24) * 0.15 * zoomY)) → G24
  35. Text(C25, (x(A) + 0.4 * zoomX, y(A) - (B25 * 10 + A25) * 0.15 * zoomY)) → G25
  36. Text(C26, (x(A) + 0.4 * zoomX, y(A) - (B26 * 10 + A26) * 0.15 * zoomY)) → G26
  37. Text("x_" * A10 * "=", (x(A), y(A) - (B10 * 10 + A10) * 0.15 * zoomY)) → F10
  38. Text("x_" * A2 * "=", (x(A), y(A) - (B2 * 10 + A2) * 0.15 * zoomY)) → F2
  39. Text("x_" * A3 * "=", (x(A), y(A) - (B3 * 10 + A3) * 0.15 * zoomY)) → F3
  40. Text("x_" * A4 * "=", (x(A), y(A) - (B4 * 10 + A4) * 0.15 * zoomY)) → F4
  41. Text("x_" * A5 * "=", (x(A), y(A) - (B5 * 10 + A5) * 0.15 * zoomY)) → F5
  42. Text("x_" * A6 * "=", (x(A), y(A) - (B6 * 10 + A6) * 0.15 * zoomY)) → F6
  43. Text("x_" * A7 * "=", (x(A), y(A) - (B7 * 10 + A7) * 0.15 * zoomY)) → F7
  44. Text("x_" * A8 * "=", (x(A), y(A) - (B8 * 10 + A8) * 0.15 * zoomY)) → F8
  45. Text("x_" * A9 * "=", (x(A), y(A) - (B9 * 10 + A9) * 0.15 * zoomY)) → F9
  46. Text(C10, (x(A) + 0.4 * zoomX, y(A) - (B10 * 10 + A10) * 0.15 * zoomY)) → G10
  47. Text(C2, (x(A) + 0.4 * zoomX, y(A) - (B2 * 10 + A2) * 0.15 * zoomY)) → G2
  48. Text(C3, (x(A) + 0.4 * zoomX, y(A) - (B3 * 10 + A3) * 0.15 * zoomY)) → G3
  49. Text(C4, (x(A) + 0.4 * zoomX, y(A) - (B4 * 10 + A4) * 0.15 * zoomY)) → G4
  50. Text(C5, (x(A) + 0.4 * zoomX, y(A) - (B5 * 10 + A5) * 0.15 * zoomY)) → G5
  51. Text(C6, (x(A) + 0.4 * zoomX, y(A) - (B6 * 10 + A6) * 0.15 * zoomY)) → G6
  52. Text(C7, (x(A) + 0.4 * zoomX, y(A) - (B7 * 10 + A7) * 0.15 * zoomY)) → G7
  53. Text(C8, (x(A) + 0.4 * zoomX, y(A) - (B8 * 10 + A8) * 0.15 * zoomY)) → G8
  54. Text(C9, (x(A) + 0.4 * zoomX, y(A) - (B9 * 10 + A9) * 0.15 * zoomY)) → G9
  55. Text(C1, (x(A) + 0.4 * zoomX, y(A))) → G1
  56. Text(C27, (x(A) + 2.1 * zoomX, y(A) - (B2 * 10 + A2) * 0.15 * zoomY)) → G27
  57. Text("x_" * B27 + "_" * A27 * "=", (x(A) + 1.7 * zoomX, y(A) - (B2 * 10 + A2) * 0.15 * zoomY)) → F27
  58. Text("x_" * B28 + "_" * A28 * "=", (x(A) + 1.7 * zoomX, y(A) - (B3 * 10 + A3) * 0.15 * zoomY)) → F28
  59. Text("x_" * B29 + "_" * A29 * "=", (x(A) + 1.7 * zoomX, y(A) - (B4 * 10 + A4) * 0.15 * zoomY)) → F29
  60. Text("x_" * B30 + "_" * A30 * "=", (x(A) + 1.7 * zoomX, y(A) - (B5 * 10 + A5) * 0.15 * zoomY)) → F30
  61. Text("x_" * B31 + "_" * A31 * "=", (x(A) + 1.7 * zoomX, y(A) - (B6 * 10 + A6) * 0.15 * zoomY)) → F31
  62. Text("x_" * B32 + "_" * A32 * "=", (x(A) + 1.7 * zoomX, y(A) - (B7 * 10 + A7) * 0.15 * zoomY)) → F32
  63. Text("x_" * B33 + "_" * A33 * "=", (x(A) + 1.7 * zoomX, y(A) - (B8 * 10 + A8) * 0.15 * zoomY)) → F33
  64. Text("x_" * B34 + "_" * A34 * "=", (x(A) + 1.7 * zoomX, y(A) - (B9 * 10 + A9) * 0.15 * zoomY)) → F34
  65. Text("x_" * B35 + "_" * A35 * "=", (x(A) + 1.7 * zoomX, y(A) - (B10 * 10 + A10) * 0.15 * zoomY)) → F35
  66. Text("x_" * B36 + "_" * A36 * "=", (x(A) + 1.7 * zoomX, y(A) - (B11 * 10 + A11) * 0.15 * zoomY)) → F36
  67. Text("x_" * B37 + "_" * A37 * "=", (x(A) + 1.7 * zoomX, y(A) - (B12 * 10 + A12) * 0.15 * zoomY)) → F37
  68. Text("x_" * B38 + "_" * A38 * "=", (x(A) + 1.7 * zoomX, y(A) - (B13 * 10 + A13) * 0.15 * zoomY)) → F38
  69. Text("x_" * B39 + "_" * A39 * "=", (x(A) + 1.7 * zoomX, y(A) - (B14 * 10 + A14) * 0.15 * zoomY)) → F39
  70. Text("x_" * B40 + "_" * A40 * "=", (x(A) + 1.7 * zoomX, y(A) - (B15 * 10 + A15) * 0.15 * zoomY)) → F40
  71. Text("x_" * B41 + "_" * A41 * "=", (x(A) + 1.7 * zoomX, y(A) - (B16 * 10 + A16) * 0.15 * zoomY)) → F41
  72. Text("x_" * B42 + "_" * A42 * "=", (x(A) + 1.7 * zoomX, y(A) - (B17 * 10 + A17) * 0.15 * zoomY)) → F42
  73. Text("x_" * B43 + "_" * A43 * "=", (x(A) + 1.7 * zoomX, y(A) - (B18 * 10 + A18) * 0.15 * zoomY)) → F43
  74. Text("x_" * B44 + "_" * A44 * "=", (x(A) + 1.7 * zoomX, y(A) - (B19 * 10 + A19) * 0.15 * zoomY)) → F44
  75. Text("x_" * B45 + "_" * A45 * "=", (x(A) + 1.7 * zoomX, y(A) - (B20 * 10 + A20) * 0.15 * zoomY)) → F45
  76. Text("x_" * B46 + "_" * A46 * "=", (x(A) + 1.7 * zoomX, y(A) - (B21 * 10 + A21) * 0.15 * zoomY)) → F46
  77. Text("x_" * B47 + "_" * A47 * "=", (x(A) + 1.7 * zoomX, y(A) - (B22 * 10 + A22) * 0.15 * zoomY)) → F47
  78. Text("x_" * B48 + "_" * A48 * "=", (x(A) + 1.7 * zoomX, y(A) - (B23 * 10 + A23) * 0.15 * zoomY)) → F48
  79. Text("x_" * B49 + "_" * A49 * "=", (x(A) + 1.7 * zoomX, y(A) - (B24 * 10 + A24) * 0.15 * zoomY)) → F49
  80. Text("x_" * B50 + "_" * A50 * "=", (x(A) + 1.7 * zoomX, y(A) - (B25 * 10 + A25) * 0.15 * zoomY)) → F50
  81. Text("x_" * B51 + "_" * A51 * "=", (x(A) + 1.7 * zoomX, y(A) - (B26 * 10 + A26) * 0.15 * zoomY)) → F51
  82. Text("x_" * B52 + "_" * A52 * "=", (x(A) + 1.7 * zoomX, y(A) - (B27 * 10 + A27) * 0.15 * zoomY)) → F52
  83. Text("x_" * B53 + "_" * A53 * "=", (x(A) + 1.7 * zoomX, y(A) - (B28 * 10 + A28) * 0.15 * zoomY)) → F53
  84. Text("x_" * B54 + "_" * A54 * "=", (x(A) + 1.7 * zoomX, y(A) - (B29 * 10 + A29) * 0.15 * zoomY)) → F54
  85. Text("x_" * B55 + "_" * A55 * "=", (x(A) + 1.7 * zoomX, y(A) - (B30 * 10 + A30) * 0.15 * zoomY)) → F55
  86. Text("x_" * B56 + "_" * A56 * "=", (x(A) + 1.7 * zoomX, y(A) - (B31 * 10 + A31) * 0.15 * zoomY)) → F56
  87. Text("x_" * B57 + "_" * A57 * "=", (x(A) + 1.7 * zoomX, y(A) - (B32 * 10 + A32) * 0.15 * zoomY)) → F57
  88. Text("x_" * B58 + "_" * A58 * "=", (x(A) + 1.7 * zoomX, y(A) - (B33 * 10 + A33) * 0.15 * zoomY)) → F58
  89. Text("x_" * B59 + "_" * A59 * "=", (x(A) + 1.7 * zoomX, y(A) - (B34 * 10 + A34) * 0.15 * zoomY)) → F59
  90. Text("x_" * B60 + "_" * A60 * "=", (x(A) + 1.7 * zoomX, y(A) - (B35 * 10 + A35) * 0.15 * zoomY)) → F60
  91. Text("x_" * B61 + "_" * A61 * "=", (x(A) + 1.7 * zoomX, y(A) - (B36 * 10 + A36) * 0.15 * zoomY)) → F61
  92. Text("x_" * B62 + "_" * A62 * "=", (x(A) + 1.7 * zoomX, y(A) - (B37 * 10 + A37) * 0.15 * zoomY)) → F62
  93. Text("x_" * B63 + "_" * A63 * "=", (x(A) + 1.7 * zoomX, y(A) - (B38 * 10 + A38) * 0.15 * zoomY)) → F63
  94. Text("x_" * B64 + "_" * A64 * "=", (x(A) + 1.7 * zoomX, y(A) - (B39 * 10 + A39) * 0.15 * zoomY)) → F64
  95. Text("x_" * B65 + "_" * A65 * "=", (x(A) + 1.7 * zoomX, y(A) - (B40 * 10 + A40) * 0.15 * zoomY)) → F65
  96. Text("x_" * B66 + "_" * A66 * "=", (x(A) + 1.7 * zoomX, y(A) - (B41 * 10 + A41) * 0.15 * zoomY)) → F66
  97. Text("x_" * B67 + "_" * A67 * "=", (x(A) + 1.7 * zoomX, y(A) - (B42 * 10 + A42) * 0.15 * zoomY)) → F67
  98. Text("x_" * B68 + "_" * A68 * "=", (x(A) + 1.7 * zoomX, y(A) - (B43 * 10 + A43) * 0.15 * zoomY)) → F68
  99. Text("x_" * B69 + "_" * A69 * "=", (x(A) + 1.7 * zoomX, y(A) - (B44 * 10 + A44) * 0.15 * zoomY)) → F69
  100. Text("x_" * B70 + "_" * A70 * "=", (x(A) + 1.7 * zoomX, y(A) - (B45 * 10 + A45) * 0.15 * zoomY)) → F70
  101. Text("x_" * B71 + "_" * A71 * "=", (x(A) + 1.7 * zoomX, y(A) - (B46 * 10 + A46) * 0.15 * zoomY)) → F71
  102. Text("x_" * B72 + "_" * A72 * "=", (x(A) + 1.7 * zoomX, y(A) - (B47 * 10 + A47) * 0.15 * zoomY)) → F72
  103. Text("x_" * B73 + "_" * A73 * "=", (x(A) + 1.7 * zoomX, y(A) - (B48 * 10 + A48) * 0.15 * zoomY)) → F73
  104. Text("x_" * B74 + "_" * A74 * "=", (x(A) + 1.7 * zoomX, y(A) - (B49 * 10 + A49) * 0.15 * zoomY)) → F74
  105. Text("x_" * B75 + "_" * A75 * "=", (x(A) + 1.7 * zoomX, y(A) - (B50 * 10 + A50) * 0.15 * zoomY)) → F75
  106. Text("x_" * B76 + "_" * A76 * "=", (x(A) + 1.7 * zoomX, y(A) - (B51 * 10 + A51) * 0.15 * zoomY)) → F76
  107. Text("x_" * B77 + "_" * A77 * "=", (x(A) + 1.7 * zoomX, y(A) - (B52 * 10 + A52) * 0.15 * zoomY)) → F77
  108. Text("x_" * B78 + "_" * A78 * "=", (x(A) + 1.7 * zoomX, y(A) - (B53 * 10 + A53) * 0.15 * zoomY)) → F78
  109. Text("x_" * B79 + "_" * A79 * "=", (x(A) + 1.7 * zoomX, y(A) - (B54 * 10 + A54) * 0.15 * zoomY)) → F79
  110. Text("x_" * B80 + "_" * A80 * "=", (x(A) + 1.7 * zoomX, y(A) - (B55 * 10 + A55) * 0.15 * zoomY)) → F80
  111. Text("x_" * B81 + "_" * A81 * "=", (x(A) + 1.7 * zoomX, y(A) - (B56 * 10 + A56) * 0.15 * zoomY)) → F81
  112. Text("x_" * B82 + "_" * A82 * "=", (x(A) + 1.7 * zoomX, y(A) - (B57 * 10 + A57) * 0.15 * zoomY)) → F82
  113. Text("x_" * B83 + "_" * A83 * "=", (x(A) + 1.7 * zoomX, y(A) - (B58 * 10 + A58) * 0.15 * zoomY)) → F83
  114. Text("x_" * B84 + "_" * A84 * "=", (x(A) + 1.7 * zoomX, y(A) - (B59 * 10 + A59) * 0.15 * zoomY)) → F84
  115. Text("x_" * B85 + "_" * A85 * "=", (x(A) + 1.7 * zoomX, y(A) - (B60 * 10 + A60) * 0.15 * zoomY)) → F85
  116. Text("x_" * B86 + "_" * A86 * "=", (x(A) + 1.7 * zoomX, y(A) - (B61 * 10 + A61) * 0.15 * zoomY)) → F86
  117. Text("x_" * B87 + "_" * A87 * "=", (x(A) + 1.7 * zoomX, y(A) - (B62 * 10 + A62) * 0.15 * zoomY)) → F87
  118. Text("x_" * B88 + "_" * A88 * "=", (x(A) + 1.7 * zoomX, y(A) - (B63 * 10 + A63) * 0.15 * zoomY)) → F88
  119. Text("x_" * B89 + "_" * A89 * "=", (x(A) + 1.7 * zoomX, y(A) - (B64 * 10 + A64) * 0.15 * zoomY)) → F89
  120. Text("x_" * B90 + "_" * A90 * "=", (x(A) + 1.7 * zoomX, y(A) - (B65 * 10 + A65) * 0.15 * zoomY)) → F90
  121. Text("x_" * B91 + "_" * A91 * "=", (x(A) + 1.7 * zoomX, y(A) - (B66 * 10 + A66) * 0.15 * zoomY)) → F91
  122. Text("x_" * B92 + "_" * A92 * "=", (x(A) + 1.7 * zoomX, y(A) - (B67 * 10 + A67) * 0.15 * zoomY)) → F92
  123. Text("x_" * B93 + "_" * A93 * "=", (x(A) + 1.7 * zoomX, y(A) - (B68 * 10 + A68) * 0.15 * zoomY)) → F93
  124. Text("x_" * B94 + "_" * A94 * "=", (x(A) + 1.7 * zoomX, y(A) - (B69 * 10 + A69) * 0.15 * zoomY)) → F94
  125. Text("x_" * B95 + "_" * A95 * "=", (x(A) + 1.7 * zoomX, y(A) - (B70 * 10 + A70) * 0.15 * zoomY)) → F95
  126. Text("x_" * B96 + "_" * A96 * "=", (x(A) + 1.7 * zoomX, y(A) - (B71 * 10 + A71) * 0.15 * zoomY)) → F96
  127. Text("x_" * B97 + "_" * A97 * "=", (x(A) + 1.7 * zoomX, y(A) - (B72 * 10 + A72) * 0.15 * zoomY)) → F97
  128. Text("x_" * B98 + "_" * A98 * "=", (x(A) + 1.7 * zoomX, y(A) - (B73 * 10 + A73) * 0.15 * zoomY)) → F98
  129. Text("x_" * B99 + "_" * A99 * "=", (x(A) + 1.7 * zoomX, y(A) - (B74 * 10 + A74) * 0.15 * zoomY)) → F99
  130. Text("x_" * B100 + "_" * A100 * "=", (x(A) + 1.7 * zoomX, y(A) - (B75 * 10 + A75) * 0.15 * zoomY)) → F100
  131. Text(C28, (x(A) + 2.1 * zoomX, y(A) - (B3 * 10 + A3) * 0.15 * zoomY)) → G28
  132. Text(C29, (x(A) + 2.1 * zoomX, y(A) - (B4 * 10 + A4) * 0.15 * zoomY)) → G29
  133. Text(C30, (x(A) + 2.1 * zoomX, y(A) - (B5 * 10 + A5) * 0.15 * zoomY)) → G30
  134. Text(C31, (x(A) + 2.1 * zoomX, y(A) - (B6 * 10 + A6) * 0.15 * zoomY)) → G31
  135. Text(C32, (x(A) + 2.1 * zoomX, y(A) - (B7 * 10 + A7) * 0.15 * zoomY)) → G32
  136. Text(C33, (x(A) + 2.1 * zoomX, y(A) - (B8 * 10 + A8) * 0.15 * zoomY)) → G33
  137. Text(C34, (x(A) + 2.1 * zoomX, y(A) - (B9 * 10 + A9) * 0.15 * zoomY)) → G34
  138. Text(C35, (x(A) + 2.1 * zoomX, y(A) - (B10 * 10 + A10) * 0.15 * zoomY)) → G35
  139. Text(C36, (x(A) + 2.1 * zoomX, y(A) - (B11 * 10 + A11) * 0.15 * zoomY)) → G36
  140. Text(C37, (x(A) + 2.1 * zoomX, y(A) - (B12 * 10 + A12) * 0.15 * zoomY)) → G37
  141. Text(C38, (x(A) + 2.1 * zoomX, y(A) - (B13 * 10 + A13) * 0.15 * zoomY)) → G38
  142. Text(C39, (x(A) + 2.1 * zoomX, y(A) - (B14 * 10 + A14) * 0.15 * zoomY)) → G39
  143. Text(C40, (x(A) + 2.1 * zoomX, y(A) - (B15 * 10 + A15) * 0.15 * zoomY)) → G40
  144. Text(C41, (x(A) + 2.1 * zoomX, y(A) - (B16 * 10 + A16) * 0.15 * zoomY)) → G41
  145. Text(C42, (x(A) + 2.1 * zoomX, y(A) - (B17 * 10 + A17) * 0.15 * zoomY)) → G42
  146. Text(C43, (x(A) + 2.1 * zoomX, y(A) - (B18 * 10 + A18) * 0.15 * zoomY)) → G43
  147. Text(C44, (x(A) + 2.1 * zoomX, y(A) - (B19 * 10 + A19) * 0.15 * zoomY)) → G44
  148. Text(C45, (x(A) + 2.1 * zoomX, y(A) - (B20 * 10 + A20) * 0.15 * zoomY)) → G45
  149. Text(C46, (x(A) + 2.1 * zoomX, y(A) - (B21 * 10 + A21) * 0.15 * zoomY)) → G46
  150. Text(C47, (x(A) + 2.1 * zoomX, y(A) - (B22 * 10 + A22) * 0.15 * zoomY)) → G47
  151. Text(C48, (x(A) + 2.1 * zoomX, y(A) - (B23 * 10 + A23) * 0.15 * zoomY)) → G48
  152. Text(C49, (x(A) + 2.1 * zoomX, y(A) - (B24 * 10 + A24) * 0.15 * zoomY)) → G49
  153. Text(C50, (x(A) + 2.1 * zoomX, y(A) - (B25 * 10 + A25) * 0.15 * zoomY)) → G50
  154. Text(C51, (x(A) + 2.1 * zoomX, y(A) - (B26 * 10 + A26) * 0.15 * zoomY)) → G51
  155. Text(C52, (x(A) + 2.1 * zoomX, y(A) - (B27 * 10 + A27) * 0.15 * zoomY)) → G52
  156. Text(C53, (x(A) + 2.1 * zoomX, y(A) - (B28 * 10 + A28) * 0.15 * zoomY)) → G53
  157. Text(C54, (x(A) + 2.1 * zoomX, y(A) - (B29 * 10 + A29) * 0.15 * zoomY)) → G54
  158. Text(C55, (x(A) + 2.1 * zoomX, y(A) - (B30 * 10 + A30) * 0.15 * zoomY)) → G55
  159. Text(C56, (x(A) + 2.1 * zoomX, y(A) - (B31 * 10 + A31) * 0.15 * zoomY)) → G56
  160. Text(C57, (x(A) + 2.1 * zoomX, y(A) - (B32 * 10 + A32) * 0.15 * zoomY)) → G57
  161. Text(C58, (x(A) + 2.1 * zoomX, y(A) - (B33 * 10 + A33) * 0.15 * zoomY)) → G58
  162. Text(C59, (x(A) + 2.1 * zoomX, y(A) - (B34 * 10 + A34) * 0.15 * zoomY)) → G59
  163. Text(C60, (x(A) + 2.1 * zoomX, y(A) - (B35 * 10 + A35) * 0.15 * zoomY)) → G60
  164. Text(C61, (x(A) + 2.1 * zoomX, y(A) - (B36 * 10 + A36) * 0.15 * zoomY)) → G61
  165. Text(C62, (x(A) + 2.1 * zoomX, y(A) - (B37 * 10 + A37) * 0.15 * zoomY)) → G62
  166. Text(C63, (x(A) + 2.1 * zoomX, y(A) - (B38 * 10 + A38) * 0.15 * zoomY)) → G63
  167. Text(C64, (x(A) + 2.1 * zoomX, y(A) - (B39 * 10 + A39) * 0.15 * zoomY)) → G64
  168. Text(C65, (x(A) + 2.1 * zoomX, y(A) - (B40 * 10 + A40) * 0.15 * zoomY)) → G65
  169. Text(C66, (x(A) + 2.1 * zoomX, y(A) - (B41 * 10 + A41) * 0.15 * zoomY)) → G66
  170. Text(C67, (x(A) + 2.1 * zoomX, y(A) - (B42 * 10 + A42) * 0.15 * zoomY)) → G67
  171. Text(C68, (x(A) + 2.1 * zoomX, y(A) - (B43 * 10 + A43) * 0.15 * zoomY)) → G68
  172. Text(C69, (x(A) + 2.1 * zoomX, y(A) - (B44 * 10 + A44) * 0.15 * zoomY)) → G69
  173. Text(C70, (x(A) + 2.1 * zoomX, y(A) - (B45 * 10 + A45) * 0.15 * zoomY)) → G70
  174. Text(C71, (x(A) + 2.1 * zoomX, y(A) - (B46 * 10 + A46) * 0.15 * zoomY)) → G71
  175. Text(C72, (x(A) + 2.1 * zoomX, y(A) - (B47 * 10 + A47) * 0.15 * zoomY)) → G72
  176. Text(C73, (x(A) + 2.1 * zoomX, y(A) - (B48 * 10 + A48) * 0.15 * zoomY)) → G73
  177. Text(C74, (x(A) + 2.1 * zoomX, y(A) - (B49 * 10 + A49) * 0.15 * zoomY)) → G74
  178. Text(C75, (x(A) + 2.1 * zoomX, y(A) - (B50 * 10 + A50) * 0.15 * zoomY)) → G75
  179. Text(C76, (x(A) + 2.1 * zoomX, y(A) - (B51 * 10 + A51) * 0.15 * zoomY)) → G76
  180. Text(C77, (x(A) + 2.1 * zoomX, y(A) - (B52 * 10 + A52) * 0.15 * zoomY)) → G77
  181. Text(C78, (x(A) + 2.1 * zoomX, y(A) - (B53 * 10 + A53) * 0.15 * zoomY)) → G78
  182. Text(C79, (x(A) + 2.1 * zoomX, y(A) - (B54 * 10 + A54) * 0.15 * zoomY)) → G79
  183. Text(C80, (x(A) + 2.1 * zoomX, y(A) - (B55 * 10 + A55) * 0.15 * zoomY)) → G80
  184. Text(C81, (x(A) + 2.1 * zoomX, y(A) - (B56 * 10 + A56) * 0.15 * zoomY)) → G81
  185. Text(C82, (x(A) + 2.1 * zoomX, y(A) - (B57 * 10 + A57) * 0.15 * zoomY)) → G82
  186. Text(C83, (x(A) + 2.1 * zoomX, y(A) - (B58 * 10 + A58) * 0.15 * zoomY)) → G83
  187. Text(C84, (x(A) + 2.1 * zoomX, y(A) - (B59 * 10 + A59) * 0.15 * zoomY)) → G84
  188. Text(C85, (x(A) + 2.1 * zoomX, y(A) - (B60 * 10 + A60) * 0.15 * zoomY)) → G85
  189. Text(C86, (x(A) + 2.1 * zoomX, y(A) - (B61 * 10 + A61) * 0.15 * zoomY)) → G86
  190. Text(C87, (x(A) + 2.1 * zoomX, y(A) - (B62 * 10 + A62) * 0.15 * zoomY)) → G87
  191. Text(C88, (x(A) + 2.1 * zoomX, y(A) - (B63 * 10 + A63) * 0.15 * zoomY)) → G88
  192. Text(C89, (x(A) + 2.1 * zoomX, y(A) - (B64 * 10 + A64) * 0.15 * zoomY)) → G89
  193. Text(C90, (x(A) + 2.1 * zoomX, y(A) - (B65 * 10 + A65) * 0.15 * zoomY)) → G90
  194. Text(C91, (x(A) + 2.1 * zoomX, y(A) - (B66 * 10 + A66) * 0.15 * zoomY)) → G91
  195. Text(C92, (x(A) + 2.1 * zoomX, y(A) - (B67 * 10 + A67) * 0.15 * zoomY)) → G92
  196. Text(C93, (x(A) + 2.1 * zoomX, y(A) - (B68 * 10 + A68) * 0.15 * zoomY)) → G93
  197. Text(C94, (x(A) + 2.1 * zoomX, y(A) - (B69 * 10 + A69) * 0.15 * zoomY)) → G94
  198. Text(C95, (x(A) + 2.1 * zoomX, y(A) - (B70 * 10 + A70) * 0.15 * zoomY)) → G95
  199. Text(C96, (x(A) + 2.1 * zoomX, y(A) - (B71 * 10 + A71) * 0.15 * zoomY)) → G96
  200. Text(C97, (x(A) + 2.1 * zoomX, y(A) - (B72 * 10 + A72) * 0.15 * zoomY)) → G97
  201. Text(C98, (x(A) + 2.1 * zoomX, y(A) - (B73 * 10 + A73) * 0.15 * zoomY)) → G98
  202. Text(C99, (x(A) + 2.1 * zoomX, y(A) - (B74 * 10 + A74) * 0.15 * zoomY)) → G99
  203. Text(C100, (x(A) + 2.1 * zoomX, y(A) - (B75 * 10 + A75) * 0.15 * zoomY)) → G100
  204. Segment((C1, C1), (C1, f(C1))) → D1
  205. Segment((C1, f(C1)), (C2, C2)) → E2
  206. Segment((C2, f(C2)), (C3, C3)) → E3
  207. Segment((C3, f(C3)), (C4, C4)) → E4
  208. Segment((C4, f(C4)), (C5, C5)) → E5
  209. Segment((C5, f(C5)), (C6, C6)) → E6
  210. Segment((C6, f(C6)), (C7, C7)) → E7
  211. Segment((C7, f(C7)), (C8, C8)) → E8
  212. Segment((C8, f(C8)), (C9, C9)) → E9
  213. Segment((C9, f(C9)), (C10, C10)) → E10
  214. Segment((C10, f(C10)), (C11, C11)) → E11
  215. Segment((C11, f(C11)), (C12, C12)) → E12
  216. Segment((C12, f(C12)), (C13, C13)) → E13
  217. Segment((C13, f(C13)), (C14, C14)) → E14
  218. Segment((C14, f(C14)), (C15, C15)) → E15
  219. Segment((C15, f(C15)), (C16, C16)) → E16
  220. Segment((C16, f(C16)), (C17, C17)) → E17
  221. Segment((C17, f(C17)), (C18, C18)) → E18
  222. Segment((C18, f(C18)), (C19, C19)) → E19
  223. Segment((C19, f(C19)), (C20, C20)) → E20
  224. Segment((C20, f(C20)), (C21, C21)) → E21
  225. Segment((C21, f(C21)), (C22, C22)) → E22
  226. Segment((C22, f(C22)), (C23, C23)) → E23
  227. Segment((C23, f(C23)), (C24, C24)) → E24
  228. Segment((C24, f(C24)), (C25, C25)) → E25
  229. Segment((C25, f(C25)), (C26, C26)) → E26
  230. Segment((C26, f(C26)), (C27, C27)) → E27
  231. Segment((C27, f(C27)), (C28, C28)) → E28
  232. Segment((C28, f(C28)), (C29, C29)) → E29
  233. Segment((C29, f(C29)), (C30, C30)) → E30
  234. Segment((C30, f(C30)), (C31, C31)) → E31
  235. Segment((C31, f(C31)), (C32, C32)) → E32
  236. Segment((C32, f(C32)), (C33, C33)) → E33
  237. Segment((C33, f(C33)), (C34, C34)) → E34
  238. Segment((C34, f(C34)), (C35, C35)) → E35
  239. Segment((C35, f(C35)), (C36, C36)) → E36
  240. Segment((C36, f(C36)), (C37, C37)) → E37
  241. Segment((C37, f(C37)), (C38, C38)) → E38
  242. Segment((C38, f(C38)), (C39, C39)) → E39
  243. Segment((C39, f(C39)), (C40, C40)) → E40
  244. Segment((C40, f(C40)), (C41, C41)) → E41
  245. Segment((C41, f(C41)), (C42, C42)) → E42
  246. Segment((C42, f(C42)), (C43, C43)) → E43
  247. Segment((C43, f(C43)), (C44, C44)) → E44
  248. Segment((C44, f(C44)), (C45, C45)) → E45
  249. Segment((C45, f(C45)), (C46, C46)) → E46
  250. Segment((C46, f(C46)), (C47, C47)) → E47
  251. Segment((C47, f(C47)), (C48, C48)) → E48
  252. Segment((C48, f(C48)), (C49, C49)) → E49
  253. Segment((C49, f(C49)), (C50, C50)) → E50
  254. Segment((C50, f(C50)), (C51, C51)) → E51
  255. Segment((C51, f(C51)), (C52, C52)) → E52
  256. Segment((C52, f(C52)), (C53, C53)) → E53
  257. Segment((C53, f(C53)), (C54, C54)) → E54
  258. Segment((C54, f(C54)), (C55, C55)) → E55
  259. Segment((C55, f(C55)), (C56, C56)) → E56
  260. Segment((C56, f(C56)), (C57, C57)) → E57
  261. Segment((C57, f(C57)), (C58, C58)) → E58
  262. Segment((C58, f(C58)), (C59, C59)) → E59
  263. Segment((C59, f(C59)), (C60, C60)) → E60
  264. Segment((C60, f(C60)), (C61, C61)) → E61
  265. Segment((C61, f(C61)), (C62, C62)) → E62
  266. Segment((C62, f(C62)), (C63, C63)) → E63
  267. Segment((C63, f(C63)), (C64, C64)) → E64
  268. Segment((C64, f(C64)), (C65, C65)) → E65
  269. Segment((C65, f(C65)), (C66, C66)) → E66
  270. Segment((C66, f(C66)), (C67, C67)) → E67
  271. Segment((C67, f(C67)), (C68, C68)) → E68
  272. Segment((C68, f(C68)), (C69, C69)) → E69
  273. Segment((C69, f(C69)), (C70, C70)) → E70
  274. Segment((C70, f(C70)), (C71, C71)) → E71
  275. Segment((C71, f(C71)), (C72, C72)) → E72
  276. Segment((C72, f(C72)), (C73, C73)) → E73
  277. Segment((C73, f(C73)), (C74, C74)) → E74
  278. Segment((C74, f(C74)), (C75, C75)) → E75
  279. Segment((C75, f(C75)), (C76, C76)) → E76
  280. Segment((C76, f(C76)), (C77, C77)) → E77
  281. Segment((C77, f(C77)), (C78, C78)) → E78
  282. Segment((C78, f(C78)), (C79, C79)) → E79
  283. Segment((C79, f(C79)), (C80, C80)) → E80
  284. Segment((C80, f(C80)), (C81, C81)) → E81
  285. Segment((C81, f(C81)), (C82, C82)) → E82
  286. Segment((C82, f(C82)), (C83, C83)) → E83
  287. Segment((C83, f(C83)), (C84, C84)) → E84
  288. Segment((C84, f(C84)), (C85, C85)) → E85
  289. Segment((C85, f(C85)), (C86, C86)) → E86
  290. Segment((C86, f(C86)), (C87, C87)) → E87
  291. Segment((C87, f(C87)), (C88, C88)) → E88
  292. Segment((C88, f(C88)), (C89, C89)) → E89
  293. Segment((C89, f(C89)), (C90, C90)) → E90
  294. Segment((C90, f(C90)), (C91, C91)) → E91
  295. Segment((C91, f(C91)), (C92, C92)) → E92
  296. Segment((C92, f(C92)), (C93, C93)) → E93
  297. Segment((C93, f(C93)), (C94, C94)) → E94
  298. Segment((C94, f(C94)), (C95, C95)) → E95
  299. Segment((C95, f(C95)), (C96, C96)) → E96
  300. Segment((C96, f(C96)), (C97, C97)) → E97
  301. Segment((C97, f(C97)), (C98, C98)) → E98
  302. Segment((C98, f(C98)), (C99, C99)) → E99
  303. Segment((C99, f(C99)), (C100, C100)) → E100
  304. Segment((C2, C2), (C2, f(C2))) → D2
  305. Segment((C3, C3), (C3, f(C3))) → D3
  306. Segment((C4, C4), (C4, f(C4))) → D4
  307. Segment((C5, C5), (C5, f(C5))) → D5
  308. Segment((C6, C6), (C6, f(C6))) → D6
  309. Segment((C7, C7), (C7, f(C7))) → D7
  310. Segment((C8, C8), (C8, f(C8))) → D8
  311. Segment((C9, C9), (C9, f(C9))) → D9
  312. Segment((C10, C10), (C10, f(C10))) → D10
  313. Segment((C11, C11), (C11, f(C11))) → D11
  314. Segment((C12, C12), (C12, f(C12))) → D12
  315. Segment((C13, C13), (C13, f(C13))) → D13
  316. Segment((C14, C14), (C14, f(C14))) → D14
  317. Segment((C15, C15), (C15, f(C15))) → D15
  318. Segment((C16, C16), (C16, f(C16))) → D16
  319. Segment((C17, C17), (C17, f(C17))) → D17
  320. Segment((C18, C18), (C18, f(C18))) → D18
  321. Segment((C19, C19), (C19, f(C19))) → D19
  322. Segment((C20, C20), (C20, f(C20))) → D20
  323. Segment((C21, C21), (C21, f(C21))) → D21
  324. Segment((C22, C22), (C22, f(C22))) → D22
  325. Segment((C23, C23), (C23, f(C23))) → D23
  326. Segment((C24, C24), (C24, f(C24))) → D24
  327. Segment((C25, C25), (C25, f(C25))) → D25
  328. Segment((C26, C26), (C26, f(C26))) → D26
  329. Segment((C27, C27), (C27, f(C27))) → D27
  330. Segment((C28, C28), (C28, f(C28))) → D28
  331. Segment((C29, C29), (C29, f(C29))) → D29
  332. Segment((C30, C30), (C30, f(C30))) → D30
  333. Segment((C31, C31), (C31, f(C31))) → D31
  334. Segment((C32, C32), (C32, f(C32))) → D32
  335. Segment((C33, C33), (C33, f(C33))) → D33
  336. Segment((C34, C34), (C34, f(C34))) → D34
  337. Segment((C35, C35), (C35, f(C35))) → D35
  338. Segment((C36, C36), (C36, f(C36))) → D36
  339. Segment((C37, C37), (C37, f(C37))) → D37
  340. Segment((C38, C38), (C38, f(C38))) → D38
  341. Segment((C39, C39), (C39, f(C39))) → D39
  342. Segment((C40, C40), (C40, f(C40))) → D40
  343. Segment((C41, C41), (C41, f(C41))) → D41
  344. Segment((C42, C42), (C42, f(C42))) → D42
  345. Segment((C43, C43), (C43, f(C43))) → D43
  346. Segment((C44, C44), (C44, f(C44))) → D44
  347. Segment((C45, C45), (C45, f(C45))) → D45
  348. Segment((C46, C46), (C46, f(C46))) → D46
  349. Segment((C47, C47), (C47, f(C47))) → D47
  350. Segment((C48, C48), (C48, f(C48))) → D48
  351. Segment((C49, C49), (C49, f(C49))) → D49
  352. Segment((C50, C50), (C50, f(C50))) → D50
  353. Segment((C51, C51), (C51, f(C51))) → D51
  354. Segment((C52, C52), (C52, f(C52))) → D52
  355. Segment((C53, C53), (C53, f(C53))) → D53
  356. Segment((C54, C54), (C54, f(C54))) → D54
  357. Segment((C55, C55), (C55, f(C55))) → D55
  358. Segment((C56, C56), (C56, f(C56))) → D56
  359. Segment((C57, C57), (C57, f(C57))) → D57
  360. Segment((C58, C58), (C58, f(C58))) → D58
  361. Segment((C59, C59), (C59, f(C59))) → D59
  362. Segment((C60, C60), (C60, f(C60))) → D60
  363. Segment((C61, C61), (C61, f(C61))) → D61
  364. Segment((C62, C62), (C62, f(C62))) → D62
  365. Segment((C63, C63), (C63, f(C63))) → D63
  366. Segment((C64, C64), (C64, f(C64))) → D64
  367. Segment((C65, C65), (C65, f(C65))) → D65
  368. Segment((C66, C66), (C66, f(C66))) → D66
  369. Segment((C67, C67), (C67, f(C67))) → D67
  370. Segment((C68, C68), (C68, f(C68))) → D68
  371. Segment((C69, C69), (C69, f(C69))) → D69
  372. Segment((C70, C70), (C70, f(C70))) → D70
  373. Segment((C71, C71), (C71, f(C71))) → D71
  374. Segment((C72, C72), (C72, f(C72))) → D72
  375. Segment((C73, C73), (C73, f(C73))) → D73
  376. Segment((C74, C74), (C74, f(C74))) → D74
  377. Segment((C75, C75), (C75, f(C75))) → D75
  378. Segment((C76, C76), (C76, f(C76))) → D76
  379. Segment((C77, C77), (C77, f(C77))) → D77
  380. Segment((C78, C78), (C78, f(C78))) → D78
  381. Segment((C79, C79), (C79, f(C79))) → D79
  382. Segment((C80, C80), (C80, f(C80))) → D80
  383. Segment((C81, C81), (C81, f(C81))) → D81
  384. Segment((C82, C82), (C82, f(C82))) → D82
  385. Segment((C83, C83), (C83, f(C83))) → D83
  386. Segment((C84, C84), (C84, f(C84))) → D84
  387. Segment((C85, C85), (C85, f(C85))) → D85
  388. Segment((C86, C86), (C86, f(C86))) → D86
  389. Segment((C87, C87), (C87, f(C87))) → D87
  390. Segment((C88, C88), (C88, f(C88))) → D88
  391. Segment((C89, C89), (C89, f(C89))) → D89
  392. Segment((C90, C90), (C90, f(C90))) → D90
  393. Segment((C91, C91), (C91, f(C91))) → D91
  394. Segment((C92, C92), (C92, f(C92))) → D92
  395. Segment((C93, C93), (C93, f(C93))) → D93
  396. Segment((C94, C94), (C94, f(C94))) → D94
  397. Segment((C95, C95), (C95, f(C95))) → D95
  398. Segment((C96, C96), (C96, f(C96))) → D96
  399. Segment((C97, C97), (C97, f(C97))) → D97
  400. Segment((C98, C98), (C98, f(C98))) → D98
  401. Segment((C99, C99), (C99, f(C99))) → D99
  402. Segment((C100, C100), (C100, f(C100))) → D100

AI 绘图提示语参考

画一个函数图像，并展示其通过重排方程为x=g(x)后的迭代过程。首先绘制函数f(x)及其导数f'(x)，然后在x轴上标记初始点x_0，接着根据迭代公式x_{n+1}=g(x_n)计算并标记后续迭代点，用文本标注每个迭代点的坐标，并用线段连接相邻点，展示迭代序列的收敛过程。
以上提示语为根据原始绘图命令整理而来，仅供参考。