![False Position Method Example:
Consider finding the root of f(x) = x2 - 3. Let εstep = 0.01, εabs = 0.01 and start
with the interval [1, 2].
12/2/2017Muhammed Mehdi
4](https://image.slidesharecdn.com/numiricalanalysis-171202100319/85/Numirical-analysis-4-320.jpg)
Numirical analysis
- 1. Numirical Analysis Presented by : Lecturer Viyan J.Jalal Prepared by : Muhammed M.Saleh 12/2/2017Muhammed Mehdi 1
- 2. Roots Of Equations A root or solutions of equation f(x)=0 are the values of x for which the equation holds true. Sometimes roots of equations are called as zeros of the equation. Numerical methods for finding roots of equations can often be easily programmed. 12/2/2017Muhammed Mehdi 2
- 3. Root Finding Methods Bisection Methods. False position methods. Secant methods. Newton-Raphson Method. Fixed-point method. Aitken method . 12/2/2017Muhammed Mehdi 3
- 4. False Position Method Example: Consider finding the root of f(x) = x2 - 3. Let εstep = 0.01, εabs = 0.01 and start with the interval [1, 2]. 12/2/2017Muhammed Mehdi 4
- 5. Newton Raphson If the initial guess at the root is xi, a tangent can be extended from the point {xi,x(xi)}. The point where this tangent crosses the x- axis usually represents an improved estimate of the root. 12/2/2017Muhammed Mehdi 5
- 6. Example F(x)=x^3-x^2-2x+1, Xo=0 ,eps 10^-6 ans=(0.4450) 12/2/2017Muhammed Mehdi 6
- 7. Aitken methods. To accelerate the convergence we compute two values D1 & D2: 𝐷1 = 𝑥0 − 𝑥1 𝐷2 = 𝑥0 − 2𝑥1 + 𝑥2 𝑋∗ = Xo − 𝐷1 2 𝐷2 12/2/2017Muhammed Mehdi 7
- 8. Example F(x)=(x+10)^(1/4) , Po=4 , eps=10^-6 find the root ? 12/2/2017Muhammed Mehdi 8
- 9. Useful Source Google-wikipida Lecture course https://www.google.iq/search?hl=ar&site=imghp&tbm 12/2/2017Muhammed Mehdi 9