What is fixed point iteration method? How can it converge to the root | Numerical Method 2079

Numerical Method20795 marksFixed point iteration and its convergence

What is fixed point iteration method? How can it converge to the root of a non-linear equation? Also explain the diverging cases with suitable examples. [5]

In the Fixed Point Iteration Method, we rearrange the non-linear equation f(x) = 0 such that x is isolated on the left-hand side of the equation. The rearranged form is expressed as: $x = g(x) \quad \cdots (1)$ Since f(x) = 0 and x = g(x) are equivalent forms, the root of f(x) = 0 is also the r...

In the Fixed Point Iteration Method, we rearrange the non-linear equation f(x) = 0 such that x is isolated on the left-hand side of the equation. The rearranged form is expressed as: $$x = g(x) \quad \cdots (1)$$ Since f(x) = 0 and x = g(x) are equivalent forms, the root of f(x) = 0 is also the r...

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