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不动点迭代

不动点迭代
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2019-08-25 19:11
函数数列解析几何
所属专题 Numerical Methods I - Root Finding
这个范例演示了不动点迭代的过程。核心数学概念包括函数和迭代。通过使用GeoGebra命令如Point、Sequence、Textfield等，可以构造出迭代过程中的点和序列。适合高中数学教学和学习。

GeoGebra 命令及参数

  1. Point(xAxis) → A
  2. Sequence(Iteration[F, x(A), i], i, 0, j) → approx
  3. Textfield(F) → InputBox1
  4. Sequence((Element[approx, i], Element[approx, i + 1]), i, 1, maxiteration + 1) → B
  5. Sequence((Element[approx, i + 1], Element[approx, i + 1]), i, 1, maxiteration) → C
  6. Vector(A, (x(A), F(x(A)))) → intialvector
  7. Point(g) → D
  8. Sequence(Vector[Element[C, i], Element[B, i + 1]], i, 1, maxiteration) → hline
  9. Sequence(Vector[Element[B, i], Element[C, i]], i, 1, maxiteration) → vline
  10. Textfield(initialvalue) → InputBox2
  11. TableText({{A1, B1}, {A2, B2}, {A3, B3}, {A4, B4}, {A5, B5}, {A6, B6}, {A7, B7}, {A8, B8}, {A9, B9}, {A10, B10}, {A11, B11}, {A12, B12}, {A13, B13}, {A14, B14}, {A15, B15}, {A16, B16}, {A17, B17}, {A18, B18}, {A19, B19}, {A20, B20}, {A21, B21}}, "|_cc") → text4