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An exponential regula falsi method

By Ben Yu

From an easy Start

S is the solution of

Define a new function

Let U(s) be a sufficiently small neighborhood of

s and s ? 0, in U(s). We can

define a function in U(s)

Do you remember

With and ,

do you remember something?

The regula falsi method

- In regula falsi method, we have f(a)f(b) lt 0
- f(x) continuous on a,b
- Get
- If f(c) lt TOL, then stop
- If f(a)f(c) lt 0, then b c
- If f(b)f(c) lt 0, then a c
- Actually, c is the estimate of the root s after

each iteration

Combine together

Algorithm

- Still need to have f(a)f(b) lt 0 and f(x)

continuous on a,b - If c ? a, b, then xn1 c and jump to the last

step - If c?a, b, then xn1 c
- If f(a)f(c) lt 0, then b c else a c
- If f(xn1) lt TOL, then stop

Example

- f(c) ln(x), a, b 0.5, 5 and start with x

1.5

Reference

- Jinhai Chen Weiguo Li An exponential regula

falsi method for solving nonlinear

equations.(2006). 41, 327-338.

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