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

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    BauerJ_2018_Final.pdf (827.5Kb)
    Author
    Bauer, Jesica
    Advisor
    Ted Wendt; Eric Sullivan; Shaun Scott
    Date of Issue
    2018-04-01
    Metadata
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    URI
    https://scholars.carroll.edu/handle/20.500.12647/3477
    Title
    More than one way to skin a cat: Interpolation techniques in one-dimension
    Type
    thesis
    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 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.
    Degree Awarded
    Bachelor's
    Semester
    Spring
    Department
    Mathematics, Engineering & Computer Science
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    • Mathematics, Engineering and Computer Science Undergraduate Theses

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