Defense Date

2024

Document Type

Thesis

Degree Name

Master of Science

Department

Mathematical Sciences

First Advisor

Dr. Laura Ellwein Fix

Abstract

One of the most studied data analysis techniques in Numerical Analysis is interpolation. Interpolation is used in a variety of fields, namely computer graphic design and biomedical research. Among interpolation techniques, cubic splines have been viewed as the standard since at least the 1960s, due to their ease of computation, numerical stability, and the relative smoothness of the interpolating curve. However, cubic splines have notable drawbacks, such as their lack of local control and necessary knowledge of boundary conditions. Arguably a more versatile interpolation technique is the use of B-splines. B-splines, a relative of Bézier curves, allow local control through knot insertion, do not require knowledge or assumption of boundary conditions for computation, and have continuous curvature. Another way to exert control on the B-spline curve is to minimize its roughness. Penalized B-splines, also called P-splines, are an emerging method of approximation and interpolation formulated in the mid-1990s by Eilers and Marx. Through definition, example, and application to cerebrovascular resistance data, we will explore the utility and benefits of P-splines.

Rights

© The Author

Is Part Of

VCU University Archives

Is Part Of

VCU Theses and Dissertations

Date of Submission

5-3-2024

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