Concept explainers
Cubic splines. Suppose you are in charge of the designof a roller coaster ride. This simple ride will not makeany left or right turns; that is, the track lies in a vertical plane. The accompanying figure shows the ride asviewed from the side. The points
One method often employed in such design problems isthe technique of cubic splines. We choose
Obviously, it is required that
Explain the practical significance of these conditions. Explain why, for the convenience of the riders, it is also required that
Show that satisfying all these conditions amounts tosolving a system of linear equations. How many variables are in this system? How many equations? (Note:It can be shown that this system has a unique solution.)
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Linear Algebra with Applications (2-Download)
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