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Approximation of a Root by First-Order Expansion
Near $$x=a$$:
$$f(x)\approx f(a)+f'(a)(x-a)$$
Setting the approximation equal to zero gives:
$$x\approx a-\frac{f(a)}{f'(a)}$$
Usage
- Provides the basis of the Newton-Raphson iteration.
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Approximation of a Root by First-Order Expansion
Near $$x=a$$:
$$f(x)\approx f(a)+f'(a)(x-a)$$
Setting the approximation equal to zero gives:
$$x\approx a-\frac{f(a)}{f'(a)}$$
Usage
- Provides the basis of the Newton-Raphson iteration.
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