Newton's Divided Difference Formula for Function Interpolation (and Forward Difference Formula)

Описание: Numerical Methods course (Numerical Analysis course) Lecture #20 at Bethel University, St. Paul, MN, Spring 2020. This is a calculus-based advanced undergraduate numerical analysis course. This video is about Newton's Divided Difference Method for function interpolation and also an introduction to Newton's Forward Difference Formula. Numerical Analysis Textbook, by Burden, Faires, and Burden: https://amzn.to/2V2f5oI

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

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(0:00) Introduction and plan
(4:17) Example 1: 3 data points
(8:14) Newton interpolation with 3 data points
(10:43) Solve for the coefficients
(14:44) Tricky algebra to generalize
(22:09) 0th, 1st, & 2nd divided differences & [ ] notation
(24:12) Tabular form
(27:24) Add a 4th node (data point)
(30:53) Simplify the 3rd degree interpolating polynomial
(31:56) Spreadsheet implementation
(33:50) The nodes don't have to be in order or equally spaced
(35:58) Divided differences in general
(38:00) Newton's forward difference formula
(47:05) Add a 4th node (data point)
(48:32) General form of Newton's forward difference formula

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