Fixed Point Iteration Q&A

[@sheesh_kebab]

Your videos are a gold mine

[@ni3cat]

your voice sounds like 3 blue 1 brown

[@mzeshan4745]

Very well explanation

[@eevibessite]

kzbin.info/www/bejne/h4nckKalfKuca7s

[@akathebest4987]

Thanks Oscar for the video! Would you be able to explain (or link to resources that explain) why |g'(x)|

[@OscarVeliz]

kzbin.info/www/bejne/rpKVp4ipjq93Y8U

[@onlinemathtutor2361]

Hey,Is all this convergence or divergence totally depend upon intial guess ?

[@OscarVeliz]

Both the initial and g(x).

[@ccuuttww]

Your last video about finding roots come form 7 years ago it is a very very very late answer what was going on for this 7 years? cast away?

[@OscarVeliz]

grad school

[@OscarVeliz]

I did respond to every question in the comments (I even made a FAQ in the description box) but I thought a video discussing them would help more than just the commenters.

[@ccuuttww]

@@OscarVeliz can U help me to find the shift in finding eigen value I stuck in QR alogrithm with shift for few days (I am idiot)most refrence book said pick shift from A(nn) element and A is in hessenberg form H-(shift)I =QR if u do this step the right bottom element become zero is it correct ?

[@OscarVeliz]

I can't help with that but if it is any consolation I'll add QR to the queue of video topics.

[@ccuuttww]

@@OscarVeliz Finally I figure it out how the shifts work for rayliegh shifts u just choose H(nxn) element for H-uI = QR H=hessberng form u = shift and H(1) = RQ+uI update shifts from H(1) in position (nxn)and continue when row(n) and column(n) are all zero or near zero pick H(n-1)(n-1) as a new shift until H matrix is in diagonal matrix This method can find all eigen value at the same time and much faster than QR alogrithm for a matrix like 4X4 it only takes 3-4 cycle for finding eigen values for wilkinson shifts just take the submatrix 2x2 matrix at the right bottom and all remain the same

[@JhonPlusse]

I think you still did not answer the first part of the last question, what is the point of this method if the root is already known, as we need it to test convergence ?

[@OscarVeliz]

That's exactly it. The test doesn't ask if it is guaranteed to converge it asks if it is guaranteed to converge to that root. To avoid the test and guesswork altogether see Wegstein's Method kzbin.info/www/bejne/ipCZnoVsp6-Lh7M

[@leesweets4110]

Is it fair to say that if youre initial guess x0 is inside of the region where |g'(x)|

[@OscarVeliz]

That is a fairly safe assumption. Sorry it has taken so long for me to respond. Some major life issues have kept me from being super active on this channel.

[@leesweets4110]

@@OscarVeliz Its all good. I appreciate the response nonetheless. I too think its a fair assumption but thats also the problem.

[@defbat7908]

Wish I found your channel earlier man.

[@eevibessite]

kzbin.info/www/bejne/h4nckKalfKuca7s

[@sufalt123]

danke shon

[@rawdhatul_fawaid]

Still confused about the root_test!

[@KHANGPHÙNGNGUYỄNAN]

❤

[@daliaruizdiaz2024]

''Find the approximate value of 3^(3/4) with the fixed point ''... How can I find the g(x) if I can't use my calculator? to put the real vAlue

[@OscarVeliz]

I'd recommend breaking 3^(3/4) into (3^(1/4))^3. This would mean what you're really trying to find is the fourth-root of 3 then cubing that result. I have an example of how to find the square-root via Newton's Method (see my videos on Newton's Method kzbin.info/www/bejne/e2OXq4h7gNaarbM and the Video Mistakes kzbin.info/www/bejne/apvaYZagmcmgeJo). You could try the same process using fixed point iteration.

[@daliaruizdiaz2024]

@@OscarVeliz thank you so much!! I've trying to find the correct function the entire afternoon :c Your channel is very helpful :)

[@ccuuttww]

your voice and speaking rhythm like 3 blue 1 brown

[@OscarVeliz]

He technically sounds like me since, as you pointed out, I started making videos quite a while ago.

[@eevibessite]

kzbin.info/www/bejne/h4nckKalfKuca7s