Chapter 04.08: Lesson: Gauss-Seidel Method of Solving Simultaneous Linear Equations: Example: Part 1

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14 жыл бұрын

Learn via example how Gauss-Seidel method of solving simultaneous linear equations works. For more videos and resources on this topic, please visit nm.mathforcollege.com/topics/g...

Пікірлер: 114

@BortPlate 9 жыл бұрын

Thank for doing what my professor wouldn't.

@5begus 4 жыл бұрын

Usually my professors notes were enough but this time he didnt give an example about this subject. This example really helped me in exam.

@kwilliams5007 8 жыл бұрын

Thank you! This really helped me prepare for my exam

@mohitdevranifromuttarakhand Жыл бұрын

Oke is gold, useful information, thank you so much

@CantoMando 7 жыл бұрын

You a lifesaver! :)

@brienooy 9 жыл бұрын

you sir! you saved me, thank you for sharing

@tchairadino 10 жыл бұрын

Nice teacher. Congratulations and thank you.

@jimshrestha3421 3 жыл бұрын

You said that people guess the initial values wrong and blabbered about it for a while without explaining exactly how to. Thanks very helpful

@askfskpsk 14 жыл бұрын

You are really a good instructor!

@EdselAdelbert 9 жыл бұрын

WOW! AMAZING. :) Thank you!

@LivingNonChalantly 12 жыл бұрын

I love this guy!! wish u were my lecturer

@manishdas6525 8 жыл бұрын

awesome job sir :)

@Peregrinans 13 жыл бұрын

Thanks from Poland ;-) It helped me a lot

@firdouszubair773 7 жыл бұрын

nice explanation... u cleared all my doubts... thanks a lotttt

@numericalmethodsguy 7 жыл бұрын

Thank you. To get even more help, go to MathForCollege.com/nm for more resources and share the link with your friends. Follow my numerical methods blog at AutarKaw.org. You can also take a free online course at www.canvas.net/?query=numerical%20methods

@davidsolomon9339 5 жыл бұрын

Thank you very much... Assuming 0.5 was a negative value (i.e -0.5) do we calculate E¹a as = -0.5-1/-0.5 ?

@5violin533 4 жыл бұрын

thanks for this video, it helps me out a lot

@firdouszubair773 7 жыл бұрын

yup.. definately I'll do share it wid my frndz....

@GinanjarUtomo 12 жыл бұрын

It's easy as hell to understand here than what my lecturer explain. Sure this helps!

@fazlisubhan3622 8 жыл бұрын

best lecture sir

@lzuha 13 жыл бұрын

thanks so much :) i like your videos..it's very helpful..

@jimmy45d 14 жыл бұрын

BRILLIANT! Thanks a lot

@AJ-et3vf 2 жыл бұрын

great video sir! Thank you!

@rybkavlad 14 жыл бұрын

Thanks. Helped a lot!!!

@MisterLazila1 11 жыл бұрын

What about diagonal dominance? Don't you need to rearrange the equations before starting so that it satisfies diagonal dominance convergence criterion?

@rocksmohit59 13 жыл бұрын

Thanks A lot... for uploading such great videos.... Ausm...

@Idontdodiplomacy 11 жыл бұрын

Excellent video. You make going to my incredibly slow paced class unnecessary :D

@liadnum 13 жыл бұрын

Thanks, From Colombia now I can do the programming

@RedDeath-kz4uw 4 жыл бұрын

You really saved me many times. Thanks you very much, sir. :D :D

@numericalmethodsguy 4 жыл бұрын

Thank you. To get even more help, subscribe to the numericalmethodsguy channel kzfaq.info, and go to MathForCollege.com/nm and MathForCollege.com/ma for more resources. Follow the numerical methods blog at AutarKaw.org. You can also take a free massive open online course (MOOC) at canvas.instructure.com/enroll/KYGTJR Share these links with your friends through social media and email.

@carlotaveas 9 жыл бұрын

Thank you so much

@deborahfranza2925 4 жыл бұрын

Why did you find the magnitude of the E or capital epsilon, the difference of the (new - initial)/new guess? I didn't understand what it was..

@numericalmethodsguy 4 жыл бұрын

The method is iterative. To know when to stop iterating, we calculate the absolute relative approximate error for each unknown. We find the maximum of these errors at the end of each step as we will have 'n' such errors at the end of an iteration. We continue to do this till the max error is less than a pre-specified tolerance. See nm.mathforcollege.com/chapter-01.02-measuring-errors and nm.mathforcollege.com/chapter-04-08-gauss-seidel-method for more info.

@kannudeol 7 жыл бұрын

Thanks you sir 👍

@thrift_vaala 2 жыл бұрын

This is soo amazing

@aceofspades3000 10 жыл бұрын

fantastic.

@MortoComeNonMai 6 жыл бұрын

Very useful!!

@drunkentabela-dt4481 3 жыл бұрын

That Whiteboard and Marker is Satisfying. 🥰

@numericalmethodsguy 3 жыл бұрын

Thank you. I love the whiteboard and marker. I miss it during the pandemic. Please subscribe and ask your friends to subscribe - our goal is to get to 100,000 subscribers by the end of 2021. To get even more help, subscribe to the numericalmethodsguy channel kzfaq.info, and go to MathForCollege.com/nm and MathForCollege.com/ma for more resources. Follow the numerical methods blog at AutarKaw.org. You can also take a free massive open online course (MOOC) at canvas.instructure.com/enroll/KYGTJR Please share these links with your friends and fellow students through social media and email.

@maffianoreen2401 4 жыл бұрын

Can you make a video for us that how to find the inital guess for the prblm

@zurc123 11 жыл бұрын

How will i know where to get my equations for x1? x2? and x3?

@Zack13IRQUSA 14 жыл бұрын

Thank you Pro.

@gummallaadityakiran591 8 жыл бұрын

should we consider [0,0,0] as initial guess if we dont have any idea of what the roots might be?.....if not what might be the best guess

@profautarkaw 8 жыл бұрын

+gummalla aditya kiran Yes, if you have no physical reason to do otherwise!

@khanthmuu6364 4 жыл бұрын

Appreciate for your sharing :)

@numericalmethodsguy 13 жыл бұрын

@tumuars90 If it is wrong, what solutions do you get? Why do you think that this is wrong!

@numericalmethodsguy 11 жыл бұрын

There is Part 2 of this video. Go to the playlists!

@gfferre302 6 жыл бұрын

you're awesome. Thanks a bunch

@numericalmethodsguy 6 жыл бұрын

Thank you. To get even more help, subscribe to the numericalmethodsguy channel, and go to MathForCollege.com/nm and MathForCollege.com/ma for more resources and share the link with your friends through social media and email. Support the site by buying the textbooks at www.lulu.com/shop/search.ep?keyWords=autar+kaw&type= Follow my numerical methods blog at AutarKaw.org. You can also take a free online course at www.canvas.net/?query=numerical%20methods

@villocan 13 жыл бұрын

Thank you from venezuela =D

@MOHAMED.HASSAN6896 6 жыл бұрын

thank you

@samuelhsfc 14 жыл бұрын

thankyou so much help me with my cw

@danrosam 12 жыл бұрын

a video on SOR would also be helpful :)

@b3llent 11 жыл бұрын

Where did you get 'initial guess' from at first place????

@thambu84 12 жыл бұрын

You are like god to me thanks a lot

@morpheus151515 12 жыл бұрын

this guy is awesome

@jamesfifa9974 6 жыл бұрын

what physics and initial order of the problem do you mean? at 1:40

@numericalmethodsguy 6 жыл бұрын

Not for this problem. Look at examples nm.mathforcollege.com/topics/gauss_seidel.html

@koolkyul 12 жыл бұрын

I do not understand the physics behind obtaining the initial guess of [1 0 1], please explain why you used this as ur initial guess

@numericalmethodsguy 11 жыл бұрын

It is not necessary to use (0,0,0) as the initial guess. In fact, many physical problems would converge faster if we knew what the solution would look like. See other comments on this video.

@43labontepetty 8 жыл бұрын

Why not x y and z? Just curious.

@numericalmethodsguy 8 жыл бұрын

We want to use vector elements as given in the video so that you can think of programming such algorithms. Imagine if you had 100 unknowns, what naming convention would you use.

@kevinmacwan7829 10 жыл бұрын

What to do when in exam there is no any type of clear cut indication of number of iteration to perform ...!!!!!

@autarkaw1826 10 жыл бұрын

Choose a pre-specified tolerance and conduct iterations till you reach that. But spend just enough time to do this to leave time for other questions on the exam.

@obinnaogx1164 9 жыл бұрын

pls why did he do the erroe calculation that gave 100 percent twice and 67.662percent thanks

@autarkaw1826 9 жыл бұрын

There are three unknowns. You need to find the absolute relative approximate error connected to each unknown. You will base the number of iterations on reducing the maximum of the three absolute relative approximate errors you get.

@m0kcun 3 жыл бұрын

how to know what to assume for the first value of x. like what u did, u start with 1 0 1. can it be any number ??

@numericalmethodsguy 3 жыл бұрын

There is no reason. I just want to dispel the myth that one needs to use the zero vector as the initial guess. In a real-life physical problem one may use the physics of the problem. Imagine a rod that is at 30 deg C and one end is held at 40 deg C and the other end at 100 deg C. If the temperatures along the rod are the unknowns in a set of simultaneous linear equations, then using this information for the initial guess will make the solution converge faster.

@m0kcun 3 жыл бұрын

@@numericalmethodsguy ohhh I see I got it nowww. Thanksss very much

@lostgen36 4 жыл бұрын

You didn't mention the diagonally dominant stuff..

@lzuha 13 жыл бұрын

thanks a lot :)

@TheGrandBrand 13 жыл бұрын

Gauss-Seidel iteration kicks major ass!

@Dobakma 6 жыл бұрын

Very nice class sir!

@jodog31 13 жыл бұрын

it clicked finally thanks

@finaljoses 11 жыл бұрын

good video

@williamherrington491 5 жыл бұрын

Thanks for not drunk driving like Kassab

@numericalmethodsguy 11 жыл бұрын

There is no place I got that from. I just want to dispel the myth that one needs to use the zero vector as the initial guess. In a real-life physical problem one may use the physics of the problem to assume the initial guess. Imagine a rod that is at 30 C and one end is held at 40C and the other end at 100 C. If the temperatures along the rod are the unknowns in a set of simultaneous linear equations, then using this information for the initial guess will make the solution converge faster.

@wahyutanlu19 7 жыл бұрын

X3 = 76-3X1 plus or minus (?) 7x2/13

@numericalmethodsguy 7 жыл бұрын

76-3*x1-...

@RiyadhSust 9 жыл бұрын

tq sir

@atifaziz279 3 жыл бұрын

dear sir 1st approximate relative error should be -100%.. m i right? please clear my confusion.. Best Regards

@numericalmethodsguy 3 жыл бұрын

What is calculated is the absolute relative approximate error!

@waldohides 11 жыл бұрын

Do more than one iteration next time please!

@numericalmethodsguy 6 жыл бұрын

See Part 2 of 2.

@numericalmethodsguy 12 жыл бұрын

See the whole playlist, especially the video on pitfalls and advantages of Gauss-Seidel Method. Go to numericalmethods(dot)eng(dot)usf(dot)edu, and click on Keyword. Click on Gauss-Seidel method and watch the videos.

@kurhulamanganyi3694 Жыл бұрын

do you have any videos on sor method

@Sublime_37 5 жыл бұрын

I wish someone would make an overrelxation video.

@jcnanaman 12 жыл бұрын

48/50 on my last exam.. 2 point deduction cause my paper dont have a name

@sercanguzel7213 10 жыл бұрын

adam işi bilen adam

@numericalmethodsguy 11 жыл бұрын

All matrices cannot be arranged. If you are going to be looking for such arrangement, you will need to write a program for that. See more details about this. Go to nm(dot)mathforcollege(dot)com and click on Keyword. Click on Gauss-Seidel method. You will see more resources.

@amberelferink 3 жыл бұрын

Why would you use this method to solve a linear equation? In this case we have 3 equations and 3 unknowns. Why not just make a matrix M * [x1, x2, x3] = [c1, c2, c3] and solve it for x1, x2, x3 by M^-1 * [c1, c2, c3] I'm trying to understand in what situations this would be a more convenient solution

@numericalmethodsguy 3 жыл бұрын

This is a long topic to discuss if you want to get to the bottom of this. Here is a short version. We are not talking about just solving 3 eqns and 3 unknowns. We use numerical methods for large set of equations. The computer time required to find the inverse of M is huge as the number of equations increases. It is proportional to n^3 as n becomes large - it can be even more time consuming if you were to use Crammer's rule to find the inverse. Gauss-Seidel method is an efficient method for many real-life problems as they have a diagonally dominant matrix M. It becomes even more efficient of the M matrix is banded - lots of zeros in the M matrix in some pattern - imagine a tridiagonal M matrix.

@amberelferink 3 жыл бұрын

@@numericalmethodsguy Thanks so much! That explains why I see it in physics simulations often while in my simple homework assignments we are told to use the inverse method