written 7.9 years ago by | modified 2.8 years ago by |

**Mumbai University > Computer Engineering > Sem 7 > Soft Computing**

**Marks:** 10 Marks

**Year:** Dec 2015

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Newton Method .

written 7.9 years ago by | modified 2.8 years ago by |

**Mumbai University > Computer Engineering > Sem 7 > Soft Computing**

**Marks:** 10 Marks

**Year:** Dec 2015

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written 7.9 years ago by |

This method is also called the tangent method. The new estimate of the root is found at the intersection between the x-axis of the line tangent to f(x) at the current state estimate of the root:

$$x_{n+1}=x_n-f{x_n}/f'{x_n}$$

This method can be viewed as a general iterative method in which the generating function $g(x)$ contains the term $h(x) = 1/f(x)$. Its drawback is the demand to know exactly the function derivation $f’(x).$

Secant method is a very economical method and can be seen as Newton’s method in which the derivation $f'{x_n}$ is replaced by its approximation.

$$x_{n+1}=x_n-f(x_n).\dfrac{x_n-x_{n-1}}{f(x_n )-f(x_{n-1})}$$

This is very useful in application, in which the function’s derivation f(x) is unknown in analytic form.

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