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Analysis and Implementation of a Method to Smooth Data Functions

Rohart, Sarah LU (2020) In Master's Theses in Mathematical Sciences MATM01 20192
Mathematics (Faculty of Engineering)
Mathematics (Faculty of Sciences)
Abstract
The goal of the thesis is to create a method that can be used to smooth data functions so that they are
more easily readable and interpretable, through curve fitting. So as to do that, we adapt the smoothing
spline method, which uses discrete data, to continuous data.
Popular Abstract
One of the most commonly found mathematical problems in engineering and science is how to create a curve
using known data points. One approach at solving those problems is the spline, a word that has its roots in
East Anglian, referencing the devices used by wood-workers to create a smooth curve. The idea was that,
in shipbuilding, thanks to the elasticity of the wood, one could apply weights - then called ducks - in certain
points, called knots or control points, and the piece of wood would bend in such a way so that it used the
least energy to bend between the knots, hence being the ”smoothest” possible.
In the same manner, and with almost exactly the same idea, splines today are functions, defined piece-wise
by polynomials, such... (More)
One of the most commonly found mathematical problems in engineering and science is how to create a curve
using known data points. One approach at solving those problems is the spline, a word that has its roots in
East Anglian, referencing the devices used by wood-workers to create a smooth curve. The idea was that,
in shipbuilding, thanks to the elasticity of the wood, one could apply weights - then called ducks - in certain
points, called knots or control points, and the piece of wood would bend in such a way so that it used the
least energy to bend between the knots, hence being the ”smoothest” possible.
In the same manner, and with almost exactly the same idea, splines today are functions, defined piece-wise
by polynomials, such that, in the case of what is called interpolating curves, they go through all the knots.
This idea was first introduced by Isaac Jacob Schoenberg, during the Second World War, which saved the
need to measure thousands of points on planes, replacing it by a more efficient mathematical model. This
model was only mathematical, and B´ezier and de Casteljau, respectively working for Renault and Citr¨oen,
eventually created stable algorithms, using it numerically for the first time, for CAD purposes.
One issue that arises numerically is that some control points are less reliable than others, and data isn’t
always perfect - hence the use of what is called smoothing splines, where the curve is only required to go
near enough every data point, depending on how reliable the data is and how smooth the result is to be.
The goal of this thesis is to adapt the spline method, which is used with discrete data, to continuous data,
so that it is not an interpolation of a great quantity of different data points, but a smoothing of a given data
function. (Less)
Please use this url to cite or link to this publication:
author
Rohart, Sarah LU
supervisor
organization
alternative title
An Adaptation of the Cubic Spline Method
course
MATM01 20192
year
type
H2 - Master's Degree (Two Years)
subject
keywords
Spline, Numerical Analysis, Mathematics, Data, Smoothing, Computer
publication/series
Master's Theses in Mathematical Sciences
report number
LUNFMA-3122-2020
ISSN
1404-6342
other publication id
2020:E85
language
English
id
9037298
date added to LUP
2023-05-31 15:21:16
date last changed
2023-05-31 15:21:16
@misc{9037298,
  abstract     = {{The goal of the thesis is to create a method that can be used to smooth data functions so that they are
more easily readable and interpretable, through curve fitting. So as to do that, we adapt the smoothing
spline method, which uses discrete data, to continuous data.}},
  author       = {{Rohart, Sarah}},
  issn         = {{1404-6342}},
  language     = {{eng}},
  note         = {{Student Paper}},
  series       = {{Master's Theses in Mathematical Sciences}},
  title        = {{Analysis and Implementation of a Method to Smooth Data Functions}},
  year         = {{2020}},
}