[alogo] Iterating cos(x)

The figure below illustrates the basic theorem for iterative procedures in calculating the roots of equations. The theorem (see Iterative.html ) is applied to the function F(x) = cos(x), with starting value x0 = 0.0. This can be easily realized with hand-held calculators (supporting the cos(x) function), which by default display the value 0.0. Press then repeatedly the "cos(x)" button to obtain the following sequence. The conditions of the referred theorem are satisfied and the the sequence converges to the number z = 0.7391... representing the ordinate of the intersection point of the graph of cos(x) with the line y = x, i.e. the solution of the equation z = cos(z).

[0_0] [0_1] [0_2] [0_3] [0_4]
[1_0] [1_1] [1_2] [1_3] [1_4]

See Also



Gisela-Jordan Engeln und Fritz Reutter Numerische Mathematik fuer Ingenieure Mannheim B.I.-Wissenschaftsverlag 1978, p. 33

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