This video looks at an example of how we can interpolate using cubic splines, both the Natural and clamped boundary conditions are considered. Text Book: Numerical Analysis by Burden, Faires & Burden
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@noel2000lw3 жыл бұрын
Best explanation on the Internet! Finally solved my problem with 4 Data-points!
@alexverwoert84442 жыл бұрын
good for u man i wish
@asifahmed18012 жыл бұрын
Thanks a lot, you have given a better explanation than any one in the internet .
@adammed86672 жыл бұрын
4th equation in the matrix, b1 should be equal to zero, and c1=-1. Anyway, thanks for the video, very very very helpful!!
@sirpsychosexy Жыл бұрын
Thank you, that had me fucked up for 30 minutes
@benjamindeworsop83484 жыл бұрын
Awesome video. No fluff, just straight explanation
@joeychou52125 жыл бұрын
Thank you so much! You made a good explanation of cubic spline. I suffer a lot from understanding the concepts in numerical analysis and using Mathematica. I hope that I could have found your videos earlier for this semester.
@SSuchti4 Жыл бұрын
one of the videos that shows me how higher math works spot on. Thank you dude, you filled wholes in my understanding i couldn't fill myself :)
@saranga46033 жыл бұрын
You saved like One and Half days of mine. Thank you
@benm93554 жыл бұрын
This video was incredibly helpful, thank you!
@davidirimia64634 жыл бұрын
You are a hero! My homework was this exact same exercise, same parameters! :D
@thiripimallarapu72274 жыл бұрын
OMG! Iam actually searching for this exact question.so,my problem is over☺☺.Thank you so much!👌👌
@iftakharalam16505 жыл бұрын
you are the best explainer among the cubic spline lecture videos. also, you are the great explainer. Thanks for making this type of video. our professors are very lazy to explain.
@the-Math-guy5 жыл бұрын
Thank you for taking the time to give such a nice comment. Appreciate it!!
@gerling-sprigadegbr8918 Жыл бұрын
Dankeschön, endlich habe ich die Lösung! Wirklich einzigartig online. Das war sehr anschaulich und die Sprachbarriere war kein Problem.
@gontle01189 ай бұрын
Thank you so much.I was struggling to understand but after your clear explanation I think I’m ready for the test👍
@sergebyusajabo21384 жыл бұрын
Good job bro. Now I understand how it is done.
@Drunk_iitian4 жыл бұрын
love you...you are the superhero...i was actually searching for this equation...
@Hansly_rz5 жыл бұрын
really helpful... calculus one professor had us do a project explaining cubic spline which is, in my opinion, way off the scale here. You saved my day thank you so much
@unsignedperson4765 жыл бұрын
You save me. Clear explanation thanks for the tip
@forzahorizon4eliminator206 Жыл бұрын
what the hell you've helped me soo much and its only today that i realized i didn't subscribe to your channel wow am sorry...and thanks for the work you are helping us a lot and making things easy for us we appreciate man
@YuzuAndGin4 жыл бұрын
Great video and clear explanation, would have really appreciated if you had simplified down the polynomials at the end.
@surjandogra6512 Жыл бұрын
Done very nicely. Only one suggestion: Show the final results in plot form and indicate on the plot different polynomials being used in different segments. Then emphasize smooth interpolation curve is created and if there are overshoots/undershoots, talk about that too. Nicely done. Thanks.
@norrisleung6665 жыл бұрын
Very nice. Learnt a lot. I think the example can be more clear if the input and output have distinct value. The polymial passing through (1,2) (2,3) (3,5), and we are considering intervals [1,2] and [2,3] (on x axis), which is kind of confusing since one may think the "2" comes from the point (1,2) and the "3" comes from the point (2,3). Anyway, great video!! Thank you
@the-Math-guy5 жыл бұрын
Thank you Norris, that is great feedback I will take that into account if I get a chance to revise this video at some point. Thank you
@norrisleung6665 жыл бұрын
@@the-Math-guy thanks for replying. Another question, i was wondering, using this method, will C0 always be 0?? Since for and point (a,b), S0(x) should have a term d0(x-a)^3, when wr apply the boundary condition, [S0(a)]´´=0 will always imply 2c0=0.
@akkismart11495 жыл бұрын
@@norrisleung666 Possibly c0 = 0 provided it satisfies the condition of natural spline. Please correct if I am wrong. check kzbin.info/www/bejne/rX6wm3ltoL2hjaM
@kevinweitgenant53003 жыл бұрын
wow. thank you. I was confused exactly by this!
@spudr21922 жыл бұрын
Yup, same here, this confused me too!
@booysenbafana43585 жыл бұрын
Thank you so much... I'm going to nail my exam today
@the-Math-guy6 жыл бұрын
Thanks Tim, appreciate it!!
@capitalp7615 жыл бұрын
how do we find the values of other unknowns? the video is great but not complete.. please share
@ajipboy5 жыл бұрын
YOU SAVE ME ! Thanks a lot!
@helenab.68935 жыл бұрын
Thank you sooo much!!! I have to write a program for Cubic Splines for university but I had no clue about Cubic Splines. This was so helpful :)
@rimshaalam24994 жыл бұрын
Hi Halena! Can you plz help my why we take only two intervals means 3 points 1 2 3 what about 5... Why we don't take this one... And how S0(1) is equal to 2? Plz reply me must...
@pauliusvainoras77874 жыл бұрын
@@rimshaalam2499 There are three points and in order to connect them we need to functions ( in previous video it's explained ). S0(1)=2, because as you see S0(x)=a0+b0(x-x0)+c0(x-x0)^2+d0(x-x0)^3, using the given data ( point (1;2) ) we know that if we input 1 we get 2. So this point is starting point so we can call it x0=1; y0=2. So function S0(x) functions between x0 and x1. So as we input x=1 to S0(1) we get =a0+b0(1-1)...=a0; also we know from data that this function node is (1;2), so S0(1)=y0=2
@albaraaabuyassen2 жыл бұрын
Man, I love you ❤
@DrWillWood3 жыл бұрын
so useful thank you!
@user-kf7pp1qh3x2 жыл бұрын
what a nice explanation! thanks
@johng52955 жыл бұрын
Thanks in a million!!!!!!!!!!!
@ummehani43443 жыл бұрын
thank you so much great work.
@juustgowithit6 жыл бұрын
You’re my savior
@the-Math-guy6 жыл бұрын
So happy to hear that!! Thank you
@Dan-id8uy5 жыл бұрын
Nicely done!
@sidrarashid55943 жыл бұрын
I Am very grateful to u very well explained and clear my topic
@packardrazor93824 жыл бұрын
Thanks bro... It's amazing explanation
@syedabishosainrizvi78172 жыл бұрын
بھای دل جیت لیا، زبردست
@hosseinkorani68075 жыл бұрын
Thanks man! Helped a lot:))
@adamm49424 жыл бұрын
How do you get the boundary conditions for s''(both 0 and 1)? is this a natural polynomial? I thought that would only work for the first derivatives being = to 0
@ahmetkarakartal95632 жыл бұрын
thank you so much
@timharig6 жыл бұрын
Underrated. Name looks foreign but speaks perfect English. All of the other videos are by Indians with strong accents. Good explanation. Please vote up.
@norrisleung6665 жыл бұрын
The "s" sound is ear piercing though...
@freezinfire Жыл бұрын
Thank you very much sir.
@baldEagle_5 жыл бұрын
cant Thank you!! in words.
@Methzvamp4 жыл бұрын
Thank you so much
@chrischoir35943 жыл бұрын
great video, but I'm just curious where did you learn this? is there some book I can buy?
@lancelofjohn69952 жыл бұрын
Nice lecture!
@TScreator7774 жыл бұрын
Thanks great help
@lordhazimuka52322 жыл бұрын
Maybe you can also tell us how you solved the augmented matrix. The rest i understand though.
Жыл бұрын
Congratulations teacher for the explanation
@byD3stroy6 жыл бұрын
Hi, thank you for this video! I've a question, how do you get the values of b0, d0, b1, etc when you got the matrix?
@GemaPratamaAditya4 жыл бұрын
vayne
@anthonyng37054 жыл бұрын
Please help, why we just have 3 points, what s about point number 5?
@sanakhanbano5 жыл бұрын
can we use the direct cubic interpolation instead of this one . can you upload direct method @themathguy
@ferdzcastle3 жыл бұрын
Great explanation. You have just accidentally interchanged the element (4,3) with element (4,4) of coefficient matrix.
@fatimazohrabechlaghem76803 жыл бұрын
Noticed the same. Was looking for a comment to point it out !
@sujatamaiti49033 жыл бұрын
Thank you sir
@sohaibkhan7796 жыл бұрын
thankyou... it helped me.. well explained
@sheikharshad75026 жыл бұрын
Sohaib Khan ap sa ya question hn gya TN plz mje btae k last matrix kse solve kia
@sheikharshad75026 жыл бұрын
Plz plz plz
@nourailham25442 жыл бұрын
What about the convergence of the estimator cubique spline ! Do you have any video or reference explain that?!!!
@pablocaiza.4 жыл бұрын
gracias amigo
@yasserhadj33353 жыл бұрын
please what is the difference between the natural and the cubic spline in terms of interpolation? does one have a bigger error than the other?
@poppyblop4843 жыл бұрын
Sorry to ask, but do you wear a cape? If not, you should, because ur a hero
@a_smile552 жыл бұрын
Thanks😄
@Adrian-sr2bu3 жыл бұрын
nice explanation
@avibank6 жыл бұрын
Awesome
@tabbycutex3 жыл бұрын
how can I solve the matrix formed on a calculator to get the values of the unknowns?
@rimshaalam24994 жыл бұрын
Can you plz help me about why you don't take interval (3,5)....and how S0(1) is equal to 2....plz reply me..
@nozomuitot10 ай бұрын
Where did the 2c0 + 6d0 = 2c1 equation in the construction of clamped cubic come from
@ajiwibowo87362 жыл бұрын
why is the second derivatiive equals to zero? doesnt it supposed to be equal each other i.e S''1(1)=S''2(3)?
@yasserothman40233 жыл бұрын
@10:09 the -1 should be in the fourth column under c1 not b1
@catherinehiggins45262 жыл бұрын
Great video man, at 8:13 why is the S"(3) and not S"(2) ? Thanks
@Cetra296 жыл бұрын
Hi, your video is awesome! It is pretty much the only thing that really helps me through this topic. I am a total newbie when it comes to splines though and need this knowledge only for one single exam and right now am really troubled when it comes to knowing when and how to use certain things. Any help would be greatly appreciated. You have used an example with three points where two overlapping spots existed. What about three points where only one point overlaps. Do I have to approach this differently or can it be done exactly the same way? I do not understand this right now but I think just doing it the same way might not lead to a satisfying conclusion? Or maybe it still is right but that's the problem, as much of a beginner I am here, I cannot really say what's adequate here. Thanks in advance!
@the-Math-guy6 жыл бұрын
Hi, thank you for the message and glad you found the video helpful. Ok in answer to your question first can you give me an example of what you have in mind for the three points with 1 overlap?
@Cetra296 жыл бұрын
Hi, wow, thank you for answering so fast. Actually I think I already found a way to solve it by understanding your video a bit more, so getting more used to the basics and then going back to check what was given to us formula-wise for the exercise. Basically it is an example where (x0, y1), (x1,y1), (x2, y2) had identical y0 and x1 like in your example the "2" is but not an identical y1 and x2 like in your example the "3" is (that is what I meant with "overlapping"; I just meant identical numbers as it seemed so important). I was wondering if its still possible to do stuff the same way but when trying out a bit more and understanding a bit more of what was given to me I saw that it is all about the same process. But definitely thank you for providing us with a video! It definitely helped!
@the-Math-guy6 жыл бұрын
Actually that has no effect on the method in my example that is just a coincidence. The method will work for any set of values but the place where the overlap is the x values. So when you connect say (x1,y1), (x2,y2) and (x3,y3) there are two splines and (x2,y2) is a part of the both splines thats the only thing to keep in mind when it comes to repeating values. Hope this makes sense. You are most welcome
@donnaguerrero55883 жыл бұрын
Good day! Can you please help me to solve having 4 data points?
@AbdulQadeer-jf7iw3 жыл бұрын
Can anybody tell why we have not taken [3,5]
@timbraunton36774 жыл бұрын
legend
@Enola8866 Жыл бұрын
why we have not taken the interval (3,5)???
@Svx_64 жыл бұрын
Cool Thanks allot
@izen42763 жыл бұрын
7:18 hard to understand how So''(1)=0?
@Queen-fl7su2 жыл бұрын
Sir plz give me one lectures of cubic non polynomial spline by differential equations
@nitnelavspetorials4 жыл бұрын
If I have to find a Quadratic Spline and I am also given the 3 points, do I have to calculate the second derivatives?
@nitnelavspetorials4 жыл бұрын
I found myself. I also knew S0'(-1) = 0, that's why I didn't need the second derivatives. VERY USEFUL VIDEO. THANKS FOR POSTING IT
@enriquesahidtenoriorodrigu8979 Жыл бұрын
Thx for everything my friend. You just got a error in yout matrix, in the 4th row you put [0,3,-1,0,0]... but is [0,3,0,-1,0] cause C1 = -1, not B1
@rememberrocko Жыл бұрын
THANK YOU! I had tried so many online matrix calculators wondering what I was missing.
@nakshathra5149 Жыл бұрын
I don't understand how u got equation 2 at 5:49
@pavelperina76293 жыл бұрын
Can you make links between some videos, it's hard to navigate from basics to next part and vice versa when videos are 4 years old.
@the-Math-guy3 жыл бұрын
Thanks for your suggestion actually if you go to the playlist for this course all videos are in sequence.
@realberkeboy2 жыл бұрын
hello first of all thanks for the video. But i didnt understand how did you find the values of b0 d0 b1... after writing the matrices. Can you explain to me? Thank you
@sandisosenzo Жыл бұрын
I haven't tried it myself yet but row reduction should give u the answer u need
@hoangthientamvuong82385 жыл бұрын
Thanks so much, it is super helpful. But I think the 4th row is not correct hmmm maybe?
@hoangthientamvuong82385 жыл бұрын
Of the matrix I mean
@the-Math-guy5 жыл бұрын
You are correct please see the little "i" in the right corner of the video there is a correction video
@musafir10686 жыл бұрын
how to implement it in Matlab for n number of data points?plz, make a video on this also.
@vimalrajayyappan20235 жыл бұрын
hey did u find a solution?
@dellarima89275 жыл бұрын
you got something wrong there, instead of c1, you write it in b1 column
@speedmetalmassiah5675 жыл бұрын
Thanks for the video, but I don't see how my professor expects us to solve a Cubic Spline, Quadratic Spline, Lagrange Polynomial, and Newton Polynomial in 1 hour.
@the-Math-guy5 жыл бұрын
Oh my sorry to hear that. Perhaps he or she thinks you are all geniuses.
@firstsecond89995 жыл бұрын
Guess I'm not the only one who thinks so too During maths exams, the time allocated does not include the time to go over the work to correct errors and that is not a good thing
@mohammedferas43936 ай бұрын
now im more confused thx
@gabrielalbu6086 жыл бұрын
Can you give me the implementation of this algorithm in Matlab ?
@the-Math-guy6 жыл бұрын
Well actually Matlab has a function coded that can do splines (quite advanced stuff). Now if you mean you want to write in Matlab or python from sort of scratch that is; well you can get a lot of pseudocode, actual code etc on the web.
@gabrielalbu6086 жыл бұрын
yeah i got the code from the web,thanks anyway for your fast response.
@abhilamsal71856 жыл бұрын
Don't we need four points in order to define a cubic function?
@the-Math-guy6 жыл бұрын
I think you are mixing things here. That is only one way to determine a cubic function. There are various other ways and certainly for cubic splines there is no such requirement.
@abhilamsal71856 жыл бұрын
oh, so cubic functions and splines are a bit different huh! thanks for clearing things up, I really appreciate it.
@EG101ify4 жыл бұрын
Why is s''(1) equal to zero?
@MUmar-tq7pr4 жыл бұрын
it is the boundary condition for natural spline
@krushnasai32496 жыл бұрын
d0 value = -1/2 i think
@the-Math-guy6 жыл бұрын
Krushna sai kumar Reddy. Thanks for your question but the solution is correct do =-1/4 not as you suggest.
@sarakisafa72833 жыл бұрын
sir, you have made a mistake, when we put fourth equation in the matrix then (-1) will come right down the (c1) not under the (b1).
@the-Math-guy3 жыл бұрын
Yes thank you I already posted a correction as a link to this video please see kzbin.info/www/bejne/q4PNimOAlt2sh8U
@nalluribharadwaj52775 жыл бұрын
the 4th row in the matrix as explained is wrong...
@the-Math-guy5 жыл бұрын
Yes thank you please see the little i in the right corner of the video for the correctiom
@Adam_mohammed_ Жыл бұрын
بطتنا بطت بطن بطتكم تقدر بطتكم تبط بطن بطتنا مثل ما بطتنا بطت بطن بطتكم!
@SuperDeadparrot Жыл бұрын
The 4th line of your matrix is wrong!
@the-Math-guy Жыл бұрын
Yes thank you I already corrected that in the video that was in more... in any case you can see it here kzbin.info/www/bejne/q4PNimOAlt2sh8U
@osmann13374 жыл бұрын
dora dan geldim bn
@kimosopjemutainasaline35413 ай бұрын
You are too fast one can't track where you are obtaining your figures
@gokselkucuksahin4 жыл бұрын
*L E A R N T O W R I T E F I R S T*
@joeysmith70214 жыл бұрын
Should pick a smaller example next time or another video with a smaller example. That is very messy
@aspiringmodernistchef4 жыл бұрын
You kidding me? This one only has 3 points, that's the "smallest" example you can have for cubic interpolation. Any "smaller" would just be 2 points, so how on earth do you do cubic interpolation on 2 points? ROFLMAO
@mahithkumar26033 жыл бұрын
Thank you so much! You made a good explanation of cubic spline. I suffer a lot from understanding the concepts in numerical analysis and using Mathematica. I hope that I could have found your videos earlier for this semester.