Piecewise Linear Interpolation and Spline Interpolation

In course

Description

This lecture covers the concepts of piecewise linear interpolation and spline interpolation. Piecewise linear interpolation involves defining points on a curve, while spline interpolation uses a function to approximate data points. The lecture discusses the stability of the interpolation methods and the convergence of errors. It also explains the process of interpolating data points using splines and the conditions for successful interpolation.

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https://mediaspace.epfl.ch/media/0_2qkcq8p1

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Definition

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Lexical definition

The lexical definition of a term, also known as the dictionary definition, is the definition closely matching the meaning of the term in common usage. As its other name implies, this is the sort of definition one is likely to find in the dictionary. A lexical definition is usually the type expected from a request for definition, and it is generally expected that such a definition will be stated as simply as possible in order to convey information to the widest audience.

Circular definition

A circular definition is a type of definition that uses the term(s) being defined as part of the description or assumes that the term(s) being described are already known. There are several kinds of circular definition, and several ways of characterising the term: pragmatic, lexicographic and linguistic. Circular definitions are related to Circular reasoning in that they both involve a self-referential approach. Circular definitions may be unhelpful if the audience must either already know the meaning of the key term, or if the term to be defined is used in the definition itself.

Theoretical definition

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Genus–differentia definition

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