QUESTION ASKED BY STUDENT: For linear splines, we still find each line individually. In quadratic, we are forced to find every equation at once, correct? Which is where the matrix comes from?

ANSWER: That sounds right, but one can find quadratic equations individually also .

How?

If the first spline is linear, then that spline can be found by the two points it goes through.

Then the second spline goes thru two points, and that gives two equations. The slope of the second spline is same as the slope of first spline at the common interior point, and the first spline is known. This gives the third eqn. This process can be repeated for each following spline.

____________________________________

This post is brought to you by Holistic Numerical Methods: Numerical Methods for the STEM undergraduate at http://nm.mathforcollege.com, the textbook on Numerical Methods with Applications available from the lulu storefront, the textbook on Introduction to Programming Concepts Using MATLAB, and the YouTube video lectures available at http://nm.mathforcollege.com/videos. Subscribe to the blog via a reader or email to stay updated with this blog. Let the information follow you.