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Fixed Point Iteration

Fixed Point Iteration
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2019-08-25 19:11
FunctionSequenceCoordinate Geometry
In collections Numerical Methods I - Root Finding
This example demonstrates the process of fixed point iteration. Key mathematical concepts include functions and iteration. Using GeoGebra commands such as Point, Sequence, and Textfield, the iteration process and points are constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  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