mathematical solution of newton raphson method

[iamlily]

 

 

 

for a given equation f(x)=x^3-8x-4

 

 

what is the first thing i should find ?

 

location of the root by the method of tabulation ?

Edited April 4, 2011 by iamlily

[timo]

It's not quite clear what you are asking for; stating what you actually want to do and writing in complete sentences might help a lot. But one promising "first thing to find" would be the derivative of your function, since it explicitly appears in the iteration scheme and is readily written down by hand.

[iamlily]

this is the method to find the tabulated x₀

 

isnt it ?

 

http://www.purplemath.com/modules/fcnnot.htm

Edited April 5, 2011 by iamlily

[timo]

I have no idea what you are asking (and pardon me for not reading the link you posted; you didn't even explain why you posted it). The Newton-Raphson algorithm is supposed to do the following (please note that what I say in the following is not strictly correct, but I hope you get the idea):

 

Assume you have a function f(x). The Newton-Raphson algorithm attempts to find an x such that f(x)=0. This is done by starting with an initial guess for x, [math]x_0[/math]. Then, you apply the Newton-Raphson step [math]x_1 = x_0 - \frac{f(x_0)}{ f'(x_0) }[/math] to get a new guess [math]x_1[/math], which hopefully is a better guess than [math]x_0[/math]. Now, to further improve this guess, you perform a Newton-Raphson step on this guess again, i.e. [math]x_2 = x_1 - \frac{f(x_1)}{ f'(x_1) } [/math]. By repeating this procedure, you successively produce better estimates for the real x.

 

If this didn't help you, then please be a bit more detailed about what your mathematical background is and what you are actually asking.

[iamlily]

first of all .. thanks for the reply .. nobody does that .. these days

 

actually i am preparing for a maths exam that deal with numerical analysis .. also called numerical methods

 

these are the stuffs in it

 

 

Bisection Method

 

 

Regula Falsi Method

 

 

Newton-Raphson

 

 

 

Solution of Linear Equation Systems

 

 

LU-Factorization

 

 

Gauss-Jordan Elimination

 

 

Gauss-Seidel Method

 

 

 

Interpolation

 

 

Numerical Differentiation

Begin with the Taylor series as seen in Equation 1.

 

 

Numerical Integration

 

 

Trapezoidal Rule

 

 

Simpson's Rule

 

 

Solution of ODEs: Initial value problems

 

 

 

Euler's Explicit Method

 

 

Runge-Kutta Methods

 

 

 

 

for a start i could write down all the formulas down .. and try to learn it ..

 

but i cant even find the formula for bisection method

Edited April 5, 2011 by iamlily

[imatfaal]

first of all .. thanks for the reply .. nobody does that .. these days

 

actually i am preparing for a maths exam that deal with numerical analysis .. also called numerical methods

 

these are the stuffs in it

 

 

Damn - I hope you have some revision time!

 

Bisection Method

uses idea that if f(a)>0 f(b)<0 then the root must lie in between

 

Find mid-point of your interval f(m) - it will then be clear that the root lies either between f(a) and f(m) OR between f(b) and f(m) as only one pair will straddle 0

 

start again with f(a) or f(b) and f(m) and find new midpoint

 

rinse and repeat

 

Will run into trouble if more than one root between the two initial guesspoints - this is the case if the curve touches the axis. Converges on a range not a value. Slow. Need continuous function

 

 

 

[iamlily]

i was thinking how about i try to copy paste all the formulas here .. for a start ..

 

i will try to fill in the formulas if i can find them .. then organize it

 

 

i will start

 

newton raphson method

 

 

 

 

 

Lagrange_interpolation_formula

 

 

 

 

 

 

 

 

Regula - falsi method

 

 

y-f(x_{0) =} f(x₁) - f(x₀)/ x_{1 -} x_{0 (}x-x₀)

 

(how do i put that big line for division ? help me fix it)

 

 

 

 

 

 

trapezoidal rule

 

 

 

 

Eulers method :

 

y_n=y_n-1+hf(x_n-1 , y _n-1)

 

 

 

 

 

Runge kutta method :

 

runge kutta method can be of different orders ...

 

 

 

 

 

will add more ..

Edited April 5, 2011 by iamlily

[imatfaal]

Lily - you might find it better to ask specific and simply worded questions rather than post large amounts of stuff that everyone knows to a greater or lesser extent. You will find people on the forum more than happy to help.

[iamlily]

Lily - you might find it better to ask specific and simply worded questions rather than post large amounts of stuff that everyone knows to a greater or lesser extent. You will find people on the forum more than happy to help. LaTeX tutorial

 

 

thanks for the LAtEx

 

this is almost impossible

 

Solution of Linear Equation Systems

 

 

LU-Factorization

 

 

Gauss-Jordan Elimination

 

 

Gauss-Seidel Method

Edited April 5, 2011 by iamlily

[imatfaal]

thanks for the LAtEx

 

this is almost impossible

 

 

 

What is? Ask simple questions and you will get answers.