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in fig 5, we show the outputs of f (without noise) and g, respectively, over the input interval [10, 10], while f and g intersect each other at x 1.38. note that in the evaluations here (and also later), the relevant (e.g., reference, biased or prediction) functions are evaluated at the points from the set {10 : 0.1 : 10}, which, following the matlab custom, represents a set of points evenly distributed over the interval [10, 10] with a span of 0.1.we first consider the problem of estimating an unknown function from given data without derivatives. we will first discuss the differentiation matrix and then present the traditional results on the topic. since the task of derivative estimation is closely related to that of simultaneous approximation, this chapter will also consider this task and its application in approximating functions from the given data in the form of {xi, liu}. we will briefly discuss the relevant theory and describe how it is implemented in matlab. this book is well-suited for readers who have completed some basic knowledge of mathematical analysis and have a working knowledge of matlab. this chapter assumes the reader is familiar with matlab and its basic functionality. for a discussion of the theoretical background of this book and a more detailed treatment of the topics of this book, we refer the reader to the appendix. for readers familiar with the various topics addressed in this chapter, the table of contents and the glossary can be used to navigate this text.
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