Fixed-point iteration method - convergence and the Fixed-point theorem

Рет қаралды 103,497

6 жыл бұрын

In this video, we look at the convergence of the method and its relation to the Fixed-point theorem. Please note there is a mistake at the end of the video 1/x-1 is not less than 1 and the iteration diverges. I will update the video.

Пікірлер: 36

@muhammadumair9020 5 жыл бұрын

The third choice is not giving values less than 1 within the given interval. Kindly rectify the solution.

@yaweli2968 3 жыл бұрын

I was about to say that,it won’t converge in the interval[1,2] even with 2 included because it doesn’t make sense to say 1

@muhammadabdulazeembaig7402 6 жыл бұрын

the third derivative is not giving value lesser than one i. e 1/(x-1), please reply,,,,

@bustro13 5 жыл бұрын

@@dentystastatysta5692 ass hole

@zzzzza7fah 5 жыл бұрын

I think this condition is sufficient but not necessary

@Antonio9648 4 жыл бұрын

Is defined as less or equal than one.

@angelineromanbautista8402 3 жыл бұрын

can I use this with fourth degree equation?

@chiomaobiajulu4363 2 жыл бұрын

when finding the derivative of g(x), what value is being used for x to check if it is less than 1 and why?

@joypaul1976 Жыл бұрын

Range of values of x, that lies between 1 and 2 in this video

@Jowhatis 7 ай бұрын

YOU ARE AMAZING THANK YOU!

@hangxu9848 Жыл бұрын

in the third derivative of g(x), it is not smaller than 1 in the interval(1,2], so it should not have a fixed point within the interval. Pls reply, I think it is an error need to be corrected.

@sirpsychosexy Жыл бұрын

agreed. please explain professor

@a_smile55 2 жыл бұрын

Thank you!

@carlosesanti6094 5 жыл бұрын

Excelent explanation! Thanks!

@stefanoaziz6092 Жыл бұрын

Why do we tak the interval between 1 and 2? I mean, one of the solutions is -0,618, so why don't we include it in the interval?

@rajnirajni120 4 жыл бұрын

Sir if f(x)=2sin(pi*x)+x and interval is [1,2] so what can be g(x) . Our teacher is suggesting us to find g(x) by newton's method can you please tell as soon as possible.

@a_smile55 2 жыл бұрын

1 year later: 🍃

@J-hk8iw Жыл бұрын

we can write x = -2sin(pi*x). In that case, g(x) = -2sin(pi*x).

@apocalypticbean 5 жыл бұрын

I dont understand what the notation means exactly

@faridjafari1710 4 жыл бұрын

Tante grazie

@wahyusuryaningrat1978 3 жыл бұрын

thanks sir

@user-cd8yi4dk6p 4 жыл бұрын

What does it mean for the derivative to be less then 1 ? Why is it important?

@the-Math-guy 4 жыл бұрын

Its a requirement of convergence that the derivative is bounded and this example demonstrates that it is less than 1 means it is bounded. It does not have to be less than 1 just less than a finite value for all x in the domain of interest. Hope that helps

@user-cd8yi4dk6p 4 жыл бұрын

@@the-Math-guy yes, I do understand it's a requirement, I just don't have the intuition for it.

@the-Math-guy 4 жыл бұрын

@@user-cd8yi4dk6p Think about it this way the derivative represents change right, and what we are doing in the iterative process is using the function g. If it changes within the band 0

@user-cd8yi4dk6p 4 жыл бұрын

@@the-Math-guy HOLY SHIT YES IT DOES

@user-cd8yi4dk6p 4 жыл бұрын

@@the-Math-guy the prove now also makes sense intuitively, if it had more than one fixed point, the function must have at least a number on which the derivative of it = 1 ( = the slop of y = ×) since those fixed points cross it, their slope is =1

@rakeshbiswas8903 Жыл бұрын

Thanks

@oumaimaabouzaid4948 6 жыл бұрын

The choice of [1,2] is based on which criterea? it's getting a little bit confusing!

@the-Math-guy 6 жыл бұрын

The [1,2] is the domain which is part of the problem and in any question it is given. So it is not chosen but given as part of the problem. Sorry about the confusion.

@oumaimaabouzaid4948 6 жыл бұрын

The Math Guy thank you so much :)

@nachimath 5 жыл бұрын

[1, 2] is the obvious choice, as f(1) = -1, f(-2) = 1 and so f(1)f(-1)