secant method

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secant method

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secant method (uncountable)

1. (mathematics) An iterative numerical method for finding a root of an equation ${\displaystyle f(x)=0}$, using a succession of roots of secant lines to better approximate the root.

It is defined by the recurrence relation ${\displaystyle x_{n+1}=x_{n}-f(x_{n}){\frac {x_{n}-x_{n-1}}{f(x_{n})-f(x_{n-1})}}}$, where ${\displaystyle n=1,2,3,...}$, and ${\displaystyle x_{0}}$ and ${\displaystyle x_{1}}$ are initial values.