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2016 | OriginalPaper | Chapter

9. Data Analysis

Author : Mark H. Holmes

Published in: Introduction to Scientific Computing and Data Analysis

Publisher: Springer International Publishing

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Abstract

In this chapter we consider a problem we have examined in earlier chapters, which is how to derive information from data. This was central to Chapter 5, when we derived interpolation formulas, and also in Chapter 8, where we investigated ways to use linear and nonlinear regression. In this chapter, four different situations are considered. The first three have a lot in common, and are examples illustrating the usefulness of the singular value decomposition (SVD) in data analysis. The SVD is explained in Section 4.5 These three methods also make use of the regression material covered in Section 8.2 The fourth method relates to what is sometimes called causal data, which means that there is an underlying mathematical model to explain the observed behavior, but it is necessary to fit the model to the data. This is similar to the regression problem, but in this case the model function comes from equations derived elsewhere, such as Newton’s laws of mechanics, or Maxwell’s equations of electrodynamics. This material will rely heavily on Section 5.4.1, which means cubic B-splines, and it uses the RK4 method, which is derived in Section 7.5

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Title: Data Analysis
Author: Mark H. Holmes
Publisher: Springer International Publishing
Book: Introduction to Scientific Computing and Data Analysis
Print ISBN: 978-3-319-30254-6

Electronic ISBN: 978-3-319-30256-0

Copyright Year: 2016
DOI: https://doi.org/10.1007/978-3-319-30256-0_9

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