Neville's Method for Interpolation is Tricky, This Video Breaks It Down Step By Step

Описание:    • Introduction to Neville's Interpolation Me...  . Numerical Methods course (Numerical Analysis course) Lecture #19 at Bethel University, St. Paul, MN, Spring 2020. This is a calculus-based advanced undergraduate numerical analysis course. Numerical Analysis Textbook, by Burden, Faires, and Burden: https://amzn.to/2V2f5oI. Amazon Prime Student 6-Month Trial: https://amzn.to/3iUKwdP. This video is about Neville's Method (Neville's Algorithm) for function interpolation, which is based on Lagrange interpolating polynomials and is pretty tricky. Neville's Method for Interpolation and Neville's Method examples are done. Neville's Method is broken down step by step and it is crucial to understand it by thinking of it as a weighted average

Lecture Documents: https://drive.google.com/drive/folder....

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(0:00) Introduction and lecture plan
(2:54) Example with 3 data points, starting with degree 0 approximations
(5:30) Linear (degree 1) approximations
(12:04) Neville's Method as a weighted average
(19:33) Quadratic (degree 2) approximation
(24:04) Weighted average again
(26:13) The general method
(29:24) Tabular representation and Q notation
(32:10) Approximating the sine function with 5 nodes
(33:23) 0th degree column
(33:57) 1st degree column
(37:51) 2nd degree column
(40:44) 3rd and 4th degree columns
(42:51) Spreadsheet (Excel) implementation
(50:45) Sample exam problem (approximate the natural logarithm)

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