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

 carrollscholars.legacy.contextkey 12327225 carrollscholars.legacy.itemurl https://scholars.carroll.edu/mathengcompsci_theses/101 carrollscholars.object.degree Bachelor's carrollscholars.object.department Mathematics, Engineering & Computer Science carrollscholars.object.disciplines Applied Mathematics; Mathematics carrollscholars.object.season Spring dc.contributor.advisor Ted Wendt dc.contributor.advisor Eric Sullivan dc.contributor.advisor Shaun Scott dc.contributor.author Bauer, Jesica dc.date.accessioned 2020-04-30T10:08:20Z dc.date.available 2020-04-30T10:08:20Z dc.date.embargo 12/31/1899 0:00 dc.date.issued 2018-04-01 dc.description.abstract In 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 BĀ“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.uri https://scholars.carroll.edu/handle/20.500.12647/3477 dc.title More than one way to skin a cat: Interpolation techniques in one-dimension dc.type thesis
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