More than one way to skin a cat: Interpolation techniques in one-dimension

carrollscholars.legacy.contextkey12327225
carrollscholars.legacy.itemurlhttps://scholars.carroll.edu/mathengcompsci_theses/101
carrollscholars.object.degreeBachelor's
carrollscholars.object.departmentMathematics, Engineering & Computer Science
carrollscholars.object.disciplinesApplied Mathematics; Mathematics
carrollscholars.object.seasonSpring
dc.contributor.advisorTed Wendt
dc.contributor.advisorEric Sullivan
dc.contributor.advisorShaun Scott
dc.contributor.authorBauer, Jesica
dc.date.accessioned2020-04-30T10:08:20Z
dc.date.available2020-04-30T10:08:20Z
dc.date.embargo12/31/1899 0:00
dc.date.issued2018-04-01
dc.description.abstractIn this paper, we discuss and develop several one-dimensional interpolation techniques. Interpolation is a process for generating functions that pass through specified points in space. In general, given a set of points P = f(x0; y0); (x1; y1); : : : ; (xn; yn)g, interpolation provides a function f(x) such that f(xi) = yi for i = 0; : : : ; n. We start by discussing common techniques used for interpolation, including polynomial, piecewise linear, cubic splines, and B´ezier curves. We also develop two new interpolation techniques: one based on a refinement of quadratic interpolation and the other based on bending properties of physical materials. We examine quantitative and qualitative errors between the existing methods and our new techniques. Finally, we discuss how the new techniques could be generalized and extended into higher dimensions.
dc.identifier.urihttps://scholars.carroll.edu/handle/20.500.12647/3477
dc.titleMore than one way to skin a cat: Interpolation techniques in one-dimension
dc.typethesis
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