MathPlotAI Logo MathPlotAI

AEF.NEC Numerical Estimation Comparison: Secant Method for Root Approximation

AEF.NEC Numerical Estimation Comparison: Secant Method for Root Approximation
Loading the math board and drawing, please wait…
2017-08-13 08:58
FunctionSequenceCalculusSlider AnimationGraphing
①This example demonstrates numerical estimation of function roots using the secant method, comparing the accuracy across different iteration counts. ②Core mathematical concepts include secant lines, root finding, iterative approximation, numerical error analysis, and the use of LCM/GCD in parameter settings. ③Construction highlights: using GeoGebra commands such as If, Line, Intersect, Point, Vector, Textfield, Segment, and Roots to build the function f, secant points, iteration sequence PAIR, and a slider n to control iterations, dynamically showing the estimated value Dif and error. ④Suitable for high school to university-level courses in numerical analysis or calculus, providing an intuitive visualization of convergence and error comparison in iterative methods.

GeoGebra Commands & Parameters

  1. If(Method ≟ 1, Iteration[NEWT[f, x(z), y(z)], z, {(a, b)}, n - 1], If[Method ≟ 2, Iteration[FPNEXT[f, x(z), y(z)], z, {(a, b)}, n - 1], Iteration[NEXTB[f, x(z), y(z)], z, {(a, b)}, n - 1]]) → PAIR
  2. Line(b_n, fb_n) → h
  3. Line(a_n, fa_n) → i
  4. Intersect(h, i) → LinearFocus
  5. Line(zero, LinearFocus) → j
  6. Line((0, x(PAIR)), (0, y(PAIR))) → c
  7. Intersect(j, c) → Secpoint
  8. Point(yAxis) → x_0
  9. Vector(x_0, B) → u
  10. Textfield(f) → inputBox1
  11. Textfield(f) → inputBox2
  12. Textfield(a) → inputBox3
  13. Textfield(b) → inputBox4
  14. Segment((y(a_n), 0), (y(b_n), 0)) → d
  15. If(Method ≠ 3, Secpoint, (0, (y(a_n) + y(b_n)) / 2)) → SecP_n
  16. Vector(SecP_n, fm_n) → mArr_n
  17. Vector(b_n, fb_n) → v
  18. Vector(a_n, fa_n) → w
  19. Roots(f, a, b) → Root,
  20. Vector(REMD, fER) → g
  21. Segment((0, x(PAIR)), (0, y(PAIR))) → k
  22. If(Method ≟ 1, text3, If[Method ≟ 2, text8, text9]) → Title