Chapter 05.03: Lesson: Newton's Divided Difference Polynomial: Quadratic Interpolation: Theory
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- Опубліковано 14 жов 2024
- Learn Newton's divided difference polynomial method by following the quadratic interpolation theory. For more videos and resources on this topic, please visit nm.mathforcolle...
Hello, the equation for b2 seems wrong if we try to derive from the above values of bo = f(xo), b1=f(x1)-f(x0)/x1-x0 . by rearranging we are getting a different equation where b2 = (f(x2)-f(x0)/x2-x0 - f(x1)-f(x0)/x1-x0) / x2 - x1 which is different from your equation .... some thing either I am missing or the b2 equation shown is wrong. pl. clarify me. The same is repeated in the Document as well. Pl. clarify. Thank you in advance. from 6.26 min to 7.39min in the video.
Of course the calculations are remaining the SAME. FYI.
+Prasad Burra Your equation is right but we want to write equations in divided difference form of f[x2,x1,x0] so that NDDP can be programmed for any order polynomial. The equation for b2 can be rewritten as (f(x2)-f(x1)/(x2-x1) - f(x1)-f(x0)/(x1-x0)) / (x2 - x0) by adding and subtracting f(x1) in the numerator and then taking f(x1)-f(x0) common. dafeda.wordpress.com/2010/09/01/newtons-divided-difference-polynomial-quadratic-interpolation/
+Prasad Burra nm.mathforcollege.com/blog/quadratic_nddp_extensive_derivation.pdf for an extensive derivation!
+numericalmethodsguy Thank you very much for the Clarification and providing the PDF with the details explaining my query. Regards. From the bottom of my heart I truly appreciate your initiative. I used these Lectures for this `Odd Semester. The best thing has been taking the same example and show casing the difference / accuracy / improvements the method brings to the solution. Thank you once again. Regards.
7.16 , when finding for the coefficient of b2 , I can't get the same answer as the given formula . Nothing was wrong in my algebraic maths . Can someone show me how they get the general formula for the coefficient of b2 ?
+Icey Junior Read this file: nm.mathforcollege.com/topics/newton_divided_difference_method.html See pages 4 and 5.
+Icey Junior nm.mathforcollege.com/blog/quadratic_nddp_extensive_derivation.pdf for an extensive derivation as promised!
+numericalmethodsguy Thank you very much ! I was looking for an explanation for this !!!!
@@numericalmethodsguy Thank you so much
can you please explain how you got f(x2) at 7:35. For some reason I get something different and the process is unclear. thanks.
Hi sir, just a confirmation, at 1:50, should the point (x2,y2) be represented by f(x2)?
Also, you're videos have helped me so very much. thanks from Canada
thank you sir i'm getting you clearly.
@r1chrd3113 Thanks, the video has an annotation now for f(x2)
Prof., have you taught cubic splines too?
Can you pls explain how you got your polynomial form? In direct method it was easy to understand because polynomial was of the form y = mx+b, which is the line, but I don't understand how you got your polynomial for NDDP
Your a great teacher, thank you
why is the f(x1) appears two times in the end of the formula ??? we had f(x0)=b0 we should have
b2(x2-X0)(x2-x1)= f(x2)- f(x0)- f(x1)-f(x0)/x1-x0 .(x2-x0) When we divide :
b2= f(x2)-f(x0)/(x2-x0)(x2-x1) - f(x1)-f(x2)/(x1-x0)(x2-x1) 1/x2-x1 ((f(x2)-f(x0)/(x2-x0) - f(x1)-f(x0)/(x1-x0))
Great video sir. thank you
Thanks from Lebanon
Thank you so much, you are a good teacher!!
How prove Pn(x) of newton equal Pn(x) of Lagrange
NDDP polynomials are chosen so that one has to solve only one equation one unknown at a time. Go to nm(dot)mathforcollege(dot)com and click on Keyword. Click on Newton's Divided Difference Polynomial. See the textbook chapter!
Thanks from Turkey:)
Thanks
thank u very much
at the end, you say you can switch the x locations to any order, and it wont affect the result, then you say you can't switch x1 and x2. ya lost me there
Thanks a lot sir :)
b2: "If you contuct the manipulation..." It seems nobody has the faintest idea about what this manipulations should be. It is not explained anywhere in literature or on the net.