Abstract
Almost all kinds of approximation are based on the principle that a complicated function is represented by a simpler function that is easy to evaluate. This simpler function has a certain number of parameters that are determined such that the approximation error is small in some sense. The finite element method for differential equations is based on this idea. In order to understand the principles, we discuss in this chapter the simpler problem of approximating a given function without any differential equations involved.
One question is how to measure the error. A very natural measure is the maximal deviation from the true function, but it turns out that the theory becomes simpler if the square of the error is integrated over the interval of interest. This leads to the least square method to be discussed in this chapter.
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© 2011 Springer-Verlag Berlin Heidelberg
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Gustafsson, B. (2011). Least Square Problems. In: Fundamentals of Scientific Computing. Texts in Computational Science and Engineering, vol 8. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19495-5_8
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DOI: https://doi.org/10.1007/978-3-642-19495-5_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-19494-8
Online ISBN: 978-3-642-19495-5
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