Quadratic Spline Interpolation: Example: Part 1 of 2
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@WhatsY0UTUB3 Thanks for your response. During these 8 months I understand it a lot better, and your message helps. Once I get this big block of work out of the way I'll get back into spline interpolation more seriously.
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I realize the comment is 8 months old and you probably understand this fully by now..
The derivatives are equal at the common point, because we can say that the function is continuous at these points. Since they are continuous at this exact point, at that instant, both splines will have an equal slope. Setting a_1 = 0 is also easily understood. As we have no previous data points, one must assume that this spline is linear.
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What about data points that form a loop? I.e. the first point is the last point. If y = [1,2,3,4,5] then y[0] = 1, y[4] = 5 and y[5] = 1 again. y[6] = 2 etc. The index thingy can easily be done using modulus operations 6%5 = 1 etc. But how can I make a spline go through those points satisfying my extra condition?
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This was a brilliant video. To a newbie like me it seems a little mad that you can simply set the derivatives to be the same at the knots and come up with 4 more equations, and the setting of "a sub 1" to be zero so we get another equation. Almost seems too easy it makes me feel uncomfortable. This video should help me understand existing splining code I am tasked to maintain.
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very well made
7:06
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Can the same approach be applied to Cubic Spline Interpolation?
divinenuker 1 year ago 2
@divinenuker Yes, it can be done by adding additional equations by equating the second derivative at the interior knots/points. However, it is better to write the cubic spline in a difference form. I do not have a reference but do a google search on "cubic spline introduction theory McKinley" and it will be the first on the list.
numericalmethodsguy 1 year ago
@numericalmethodsguy will you be doing a video on cubic spline interpolation?
sangboi 1 year ago
@sangboi Not in the near future.
numericalmethodsguy 1 year ago
whats the easiest method for solving the 15x15 matrix by hand?
489305004 2 years ago
You can use Gaussian elimination. Doing a 15x15 by hand is not recommended.
numericalmethodsguy 2 years ago