When I was 4 years old, this video was made. Now, after one and a half decades, watching it brings back so many memories and emotions from my childhood
This is really great. Not only am I getting information about what I really want to learn about (polynomial interpolation, splines, etc), I'm getting a chance to put into practice my previous learning (from Khan Academy and a 3D game programming book) about using matrices to solve systems of linear equations. What I learnt there has faded from memory a bit so I can hopefully pull it all together.
@agravesf The second order derivatives are also continuous at the interior data points. 6 points - 5 splines - 20 unknowns. Each spline goes thru two consecutive pts - 10 eqns, splines have 1st derivative continuous at interior pts - 4 eqns, splines have 2nd derivative continuous at interior pts - 4 eqns, first spline is quadratic and last spline is quadratic - 2 eqns. Total 20eqns.
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You need to use quadratic or cubic spline interpolation to maintain continuation of derivatives at the interior points. Quadratic will maintain continuity of first derivative, while cubic spline will maintain continuity of first and second derivative. Go to nm(dot)mathforcollege(dot)com and click on Keyword. Click on Quadratic Spline Interpolation. You will see all the videos and more resources.
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.
I suspect that is it, everytime the power of the polinomial increases we then define one more point as part of the function. For the quadratic you used two points, but I think that i will need to use 3 for the cubic and so on. This will then give me 15 equations in step 1), which will then allow me to assume in step 3) that my process starts with a qquadratic function.
Can I use this method to make a smooth line when I have data of some points? I got my task done with quadratic interpolation, and I wonder if I can get better results with cubic one since it uses more information to find value between given points. My question from the other side: if I count a0, a1, a2, a3 for every spline and build a graph, will it break in given point or will it be smooth? (Will the speed of the function BEFORE the given point be EQUAL to one right AFTER the given point?)
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
while calculating the relative error why did you use the result form cubic and not quadratic? aren't we calculating the error of the result from cubic relative to that from quadratic?? o.O
I am studying about Numerical Analysis. But this video talk about cubic spline, you use 4 equations with 4 unknowns, I think it is problem. It is so easy, you can explain
ปิยวัช คุณทรงเกียรติ You would choose t=0, 10, 15, 20 as the 4 points to conduct cubic interpolation. The choice of points is based on making sure that the point of interest is bracketed and also that they are the closest points.
2) now we have left 10 euqations to find if we now make the derivatives equal at the interior points we will be able to get 4 equations 3) if we now force two of the functions parameters say a1=0 and b1=0, such that the first function is linear Now I still have left 4 equations to be found... !!!!! So where am I going wrong? This has made me question step 1) and if it is in fact every two points that we have a defined function... ...continue next post...
I am struggling to derive this same solution (set of equations) for a cubic spline. Ok, here is my doubt, it is more conceptually actually. When we solve for local polynomials we need: Linear: we need two points (x1,y1) and (x2,y2) thus 2 equations. Quadratic: we need at least three data points (x1,y1), (x2,y2), (x3,y3), thus 3 equations. Cubic: we need at least four data points (x1,y1), (x2,y2), (x3,y3), (x4,y4), thus 4 equations ... continue in next post...
YET WHEN in the spline method we say that: 1) every two point we have one function, hence #functions = n # functions * (polynomial power+1) = unknowns On the cubic case we therefore have: n*4, in your exmaple n=5, therefore 20 unknowns. If every two points we have one function and each point can comply with two different functions the we are able to generate 2 equations per interior points and one equation per extreme points, we are able to get 10 equations. ...continue next post..
@YourWorstNightmareDK May I suggest going to the numericalmethods(dot)eng(dot)usf(dot)edu website, click on keyword, click on Matrix Algebra. That will bring your weak side to a strong side.
When I was 4 years old, this video was made. Now, after one and a half decades, watching it brings back so many memories and emotions from my childhood
Good to hear. I hope all the memories and emotions were good.
This is really great. Not only am I getting information about what I really want to learn about (polynomial interpolation, splines, etc), I'm getting a chance to put into practice my previous learning (from Khan Academy and a 3D game programming book) about using matrices to solve systems of linear equations. What I learnt there has faded from memory a bit so I can hopefully pull it all together.
@agravesf The second order derivatives are also continuous at the interior data points.
6 points - 5 splines - 20 unknowns. Each spline goes thru two consecutive pts - 10 eqns, splines have 1st derivative continuous at interior pts - 4 eqns, splines have 2nd derivative continuous at interior pts - 4 eqns, first spline is quadratic and last spline is quadratic - 2 eqns. Total 20eqns.
This made me subscribe :) Only video explaining it simply, clearly , directly
We calculate relative error based on current approx (cubic) and previous approximation (quadratic) as epsa=abs((current-previous)/current)*100
Tanks so much , i not find a vídeo on youtube in portuguese , so your vídeo was my last hope , and i understand everthing...
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. Follow my numerical methods blog at AutarKaw.org. You can also take a free online course at www.canvas.net/?query=numerical%20methods
You need to use quadratic or cubic spline interpolation to maintain continuation of derivatives at the interior points. Quadratic will maintain continuity of first derivative, while cubic spline will maintain continuity of first and second derivative. Go to nm(dot)mathforcollege(dot)com and click on Keyword. Click on Quadratic Spline Interpolation. You will see all the videos and more resources.
Sir ur English is very good to listen
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.
Hello Sir,
Could you please tell me the main differnce between cubic spine and cubic interpolation?
I suspect that is it, everytime the power of the polinomial increases we then define one more point as part of the function. For the quadratic you used two points, but I think that i will need to use 3 for the cubic and so on.
This will then give me 15 equations in step 1), which will then allow me to assume in step 3) that my process starts with a qquadratic function.
Can I use this method to make a smooth line when I have data of some points? I got my task done with quadratic interpolation, and I wonder if I can get better results with cubic one since it uses more information to find value between given points. My question from the other side: if I count a0, a1, a2, a3 for every spline and build a graph, will it break in given point or will it be smooth? (Will the speed of the function BEFORE the given point be EQUAL to one right AFTER the given point?)
sir can u please make videos about cubic splines.
Nice and easy example.
sir awesome.....
thank you so much
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
This is the khan academy of numerical methods/analysis. You should partner up!
while calculating the relative error why did you use the result form cubic and not quadratic?
aren't we calculating the error of the result from cubic relative to that from quadratic?? o.O
Hello sir,why could we say that 3 digital are correct?
Ok, got it! Thanks for your help!
Cubic splines are different from cubic interpolation. I do not have a video on it.
ca you share a link to it.?
I am studying about Numerical Analysis. But this video talk about cubic spline, you use 4 equations with 4 unknowns, I think it is problem. It is so easy, you can explain
This is great, thanks
Thankyou!
Sir plz give me lecture of cubic non polynomial spline by differential equations
how about f(5)? how to calculate?
ปิยวัช คุณทรงเกียรติ You would choose t=0, 10, 15, 20 as the 4 points to conduct cubic interpolation. The choice of points is based on making sure that the point of interest is bracketed and also that they are the closest points.
2) now we have left 10 euqations to find
if we now make the derivatives equal at the interior points we will be able to get 4 equations
3) if we now force two of the functions parameters say a1=0 and b1=0, such that the first function is linear
Now I still have left 4 equations to be found... !!!!!
So where am I going wrong?
This has made me question step 1) and if it is in fact every two points that we have a defined function...
...continue next post...
I am struggling to derive this same solution (set of equations) for a cubic spline.
Ok, here is my doubt, it is more conceptually actually.
When we solve for local polynomials we need:
Linear: we need two points (x1,y1) and (x2,y2) thus 2 equations.
Quadratic: we need at least three data points (x1,y1), (x2,y2), (x3,y3), thus 3 equations.
Cubic: we need at least four data points (x1,y1), (x2,y2), (x3,y3), (x4,y4), thus 4 equations
... continue in next post...
YET WHEN in the spline method we say that:
1) every two point we have one function, hence #functions = n
# functions * (polynomial power+1) = unknowns
On the cubic case we therefore have: n*4, in your exmaple n=5, therefore 20 unknowns.
If every two points we have one function and each point can comply with two different functions the we are able to generate 2 equations per interior points and one equation per extreme points, we are able to get 10 equations.
...continue next post..
@YourWorstNightmareDK May I suggest going to the numericalmethods(dot)eng(dot)usf(dot)edu website, click on keyword, click on Matrix Algebra. That will bring your weak side to a strong side.
kindly declare the methods to find all the unknowns a0a1a2a3
I solved it by elimination... But the answers are change of four unknowns....????
There????
sir can u please make videos about cubic splines.