Interpolation - Cubic Splines - example

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

[@noel2000lw]

Best explanation on the Internet! Finally solved my problem with 4 Data-points!

[@alexverwoert8444]

good for u man i wish

[@asifahmed1801]

Thanks a lot, you have given a better explanation than any one in the internet .

[@adammed8667]

4th equation in the matrix, b1 should be equal to zero, and c1=-1. Anyway, thanks for the video, very very very helpful!!

[@sirpsychosexy]

Thank you, that had me fucked up for 30 minutes

[@joeychou5212]

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.

[@benjamindeworsop8348]

Awesome video. No fluff, just straight explanation

[@SSuchti4]

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 :)

[@davidirimia6463]

You are a hero! My homework was this exact same exercise, same parameters! :D

[@benm9355]

This video was incredibly helpful, thank you!

[@saranga4603]

You saved like One and Half days of mine. Thank you

[@iftakharalam1650]

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-guy]

Thank you for taking the time to give such a nice comment. Appreciate it!!

[@thiripimallarapu7227]

OMG! Iam actually searching for this exact question.so,my problem is over☺☺.Thank you so much!👌👌

[@gerling-sprigadegbr8918]

Dankeschön, endlich habe ich die Lösung! Wirklich einzigartig online. Das war sehr anschaulich und die Sprachbarriere war kein Problem.

[@gontle0118]

Thank you so much.I was struggling to understand but after your clear explanation I think I’m ready for the test👍

[@norrisleung666]

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-guy]

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

[@norrisleung666]

@@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.

[@akkismart1149]

@@norrisleung666 Possibly c0 = 0 provided it satisfies the condition of natural spline. Please correct if I am wrong. check kzbin.info/www/bejne/rX6wm3ltoL2hjaM

[@kevinweitgenant5300]

wow. thank you. I was confused exactly by this!

[@spudr2192]

Yup, same here, this confused me too!

[@Hansly_rz]

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

[@Drunk_iitian]

love you...you are the superhero...i was actually searching for this equation...

[@unsignedperson476]

You save me. Clear explanation thanks for the tip

[@helenab.6893]

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 :)

[@rimshaalam2499]

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...

[@pauliusvainoras7787]

@@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

[@forzahorizon4eliminator206]

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

[@surjandogra6512]

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.

[@sergebyusajabo2138]

Good job bro. Now I understand how it is done.

[@YuzuAndGin]

Great video and clear explanation, would have really appreciated if you had simplified down the polynomials at the end.

[@adamm4942]

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

[@the-Math-guy]

Thanks Tim, appreciate it!!

[@capitalp761]

how do we find the values of other unknowns? the video is great but not complete.. please share

[@chrischoir3594]

great video, but I'm just curious where did you learn this? is there some book I can buy?

[@byD3stroy]

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?

[@GemaPratamaAditya]

vayne

[@syedabishosainrizvi7817]

بھای دل جیت لیا، زبردست

[@timharig]

Underrated. Name looks foreign but speaks perfect English. All of the other videos are by Indians with strong accents. Good explanation. Please vote up.

[@norrisleung666]

The "s" sound is ear piercing though...

[@anthonyng3705]

Please help, why we just have 3 points, what s about point number 5?

[@ajipboy]

YOU SAVE ME ! Thanks a lot!

[@booysenbafana4358]

Thank you so much... I'm going to nail my exam today

[@DrWillWood]

so useful thank you!

[@sanakhanbano]

can we use the direct cubic interpolation instead of this one . can you upload direct method @themathguy

[@ummehani4344]

thank you so much great work.

[@lordhazimuka5232]

Maybe you can also tell us how you solved the augmented matrix. The rest i understand though.

[@user-kf7pp1qh3x]

what a nice explanation! thanks

[@johng5295]

Thanks in a million!!!!!!!!!!!

[@poppyblop484]

Sorry to ask, but do you wear a cape? If not, you should, because ur a hero

[@hosseinkorani6807]

Thanks man! Helped a lot:))

[@Dan-id8uy]

Nicely done!

[@nourailham2544]

What about the convergence of the estimator cubique spline ! Do you have any video or reference explain that?!!!

[@tabbycutex]

how can I solve the matrix formed on a calculator to get the values of the unknowns?

[@albaraaabuyassen]

Man, I love you ❤

[@juustgowithit]

You’re my savior

[@the-Math-guy]

So happy to hear that!! Thank you

[@yasserhadj3335]

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?

[@sidrarashid5594]

I Am very grateful to u very well explained and clear my topic

[@rimshaalam2499]

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..

[@ajiwibowo8736]

why is the second derivatiive equals to zero? doesnt it supposed to be equal each other i.e S''1(1)=S''2(3)?

[@nozomuitot]

Where did the 2c0 + 6d0 = 2c1 equation in the construction of clamped cubic come from

[@packardrazor9382]

Thanks bro... It's amazing explanation

[@baldEagle_]

cant Thank you!! in words.

[@Cetra29]

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-guy]

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?

[@Cetra29]

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-guy]

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

Congratulations teacher for the explanation

[@ferdzcastle]

Great explanation. You have just accidentally interchanged the element (4,3) with element (4,4) of coefficient matrix.

[@fatimazohrabechlaghem7680]

Noticed the same. Was looking for a comment to point it out !

[@Methzvamp]

Thank you so much

[@ahmetkarakartal9563]

thank you so much

[@donnaguerrero5588]

Good day! Can you please help me to solve having 4 data points?

[@sohaibkhan779]

thankyou... it helped me.. well explained

[@sheikharshad7502]

Sohaib Khan ap sa ya question hn gya TN plz mje btae k last matrix kse solve kia

[@sheikharshad7502]

Plz plz plz

[@TScreator777]

Thanks great help

[@freezinfire]

Thank you very much sir.

[@catherinehiggins4526]

Great video man, at 8:13 why is the S"(3) and not S"(2) ? Thanks

[@AbdulQadeer-jf7iw]

Can anybody tell why we have not taken [3,5]

[@izen4276]

7:18 hard to understand how So''(1)=0?

[@lancelofjohn6995]

Nice lecture!

[@Enola8866]

why we have not taken the interval (3,5)???

[@nitnelavspetorials]

If I have to find a Quadratic Spline and I am also given the 3 points, do I have to calculate the second derivatives?

[@nitnelavspetorials]

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

[@avibank]

Awesome

[@sujatamaiti4903]

Thank you sir

[@realberkeboy]

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]

I haven't tried it myself yet but row reduction should give u the answer u need

[@pavelperina7629]

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-guy]

Thanks for your suggestion actually if you go to the playlist for this course all videos are in sequence.

[@pablocaiza.]

gracias amigo

[@Adrian-sr2bu]

nice explanation

[@a_smile55]

Thanks😄

[@yasserothman4023]

@10:09 the -1 should be in the fourth column under c1 not b1

[@Queen-fl7su]

Sir plz give me one lectures of cubic non polynomial spline by differential equations

[@nakshathra5149]

I don't understand how u got equation 2 at 5:49

[@musafir1068]

how to implement it in Matlab for n number of data points?plz, make a video on this also.

[@vimalrajayyappan2023]

hey did u find a solution?

[@enriquesahidtenoriorodrigu8979]

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]

THANK YOU! I had tried so many online matrix calculators wondering what I was missing.

[@hoangthientamvuong8238]

Thanks so much, it is super helpful. But I think the 4th row is not correct hmmm maybe?

[@hoangthientamvuong8238]

Of the matrix I mean

[@the-Math-guy]

You are correct please see the little "i" in the right corner of the video there is a correction video

[@Svx_6]

Cool Thanks allot

[@gabrielalbu608]

Can you give me the implementation of this algorithm in Matlab ?

[@the-Math-guy]

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.

[@gabrielalbu608]

yeah i got the code from the web,thanks anyway for your fast response.

[@speedmetalmassiah567]

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-guy]

Oh my sorry to hear that. Perhaps he or she thinks you are all geniuses.

[@firstsecond8999]

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

[@timbraunton3677]

legend

[@dellarima8927]

you got something wrong there, instead of c1, you write it in b1 column

[@EG101ify]

Why is s''(1) equal to zero?

[@MUmar-tq7pr]

it is the boundary condition for natural spline

[@abhilamsal7185]

Don't we need four points in order to define a cubic function?

[@the-Math-guy]

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.

[@abhilamsal7185]

oh, so cubic functions and splines are a bit different huh! thanks for clearing things up, I really appreciate it.

[@krushnasai3249]

d0 value = -1/2 i think

[@the-Math-guy]

Krushna sai kumar Reddy. Thanks for your question but the solution is correct do =-1/4 not as you suggest.

[@nalluribharadwaj5277]

the 4th row in the matrix as explained is wrong...

[@the-Math-guy]

Yes thank you please see the little i in the right corner of the video for the correctiom

[@mohammedferas4393]

now im more confused thx

[@sarakisafa7283]

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-guy]

Yes thank you I already posted a correction as a link to this video please see kzbin.info/www/bejne/q4PNimOAlt2sh8U

[@Adam_mohammed_]

بطتنا بطت بطن بطتكم تقدر بطتكم تبط بطن بطتنا مثل ما بطتنا بطت بطن بطتكم!

[@SuperDeadparrot]

The 4th line of your matrix is wrong!

[@the-Math-guy]

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

[@joeysmith7021]

Should pick a smaller example next time or another video with a smaller example. That is very messy

[@aspiringmodernistchef]

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

[@kimosopjemutainasaline3541]

You are too fast one can't track where you are obtaining your figures

[@osmann1337]

dora dan geldim bn

[@gokselkucuksahin]

*L E A R N T O W R I T E F I R S T*

[@mahithkumar2603]

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.