Module II: Polynomial interpolation

Given a sequence of nodal locations x, and data values f, we aim to interpolate this data - that is find a function p(x) (the interpolant that passes (exactly) through all the data points. This is the interpolation problem. We explore the use of polynomials to represent the function p(x), and ask questions about existance and uniqueness of p(x). In the case that the data originates from an underlying function f(x), we can ask under what circumstances p(x) is a good approximation of f(x) - i.e. we develop estimates of the error in p(x). Finally we touch briefly on the important topic of regression.

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Supporting reader: Section 3.0

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Supporting reader: Sections 3.0, 3.1

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Supporting reader: Example 3.2

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Supporting reader: Theorem 3.5

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Supporting reader: n/a

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Supporting reader: Section 3.0

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Supporting reader: Section 3.4

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Supporting reader: Sections 3.2, 3.5

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Supporting reader: n/a

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Supporting reader: Theorem 3.10, Section 3.5.1

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0:50 - A small inconsistency: I use \(\omega_N\) to refer to the nodal polynomial of degree \(N+1\). In previous videos I used \(\omega_{N+1}\) to refer to the same thing. This is just a notational incosistency, they refer to the same object.

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Supporting reader: Chapter 5

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Total time: 3:04:00

dr. R. Dwight ≤r.p.dwight@tudelft.nl≥ - 2022-02-15