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zaltac authored Jan 14, 2025
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[Video 1. Lagrange Polynomials and Lagrange Interpolation](https://youtube.com/video/qsnGXWvEnD0) This video covers theoretical aspects of constructing Lagrange basis polynomials and Lagrange interpolating function. A numerical example involving interpolation of a discrete dataset is presented step by step.

[Video 2. Newton's Divided Difference](https://youtu.be/a8i4Xn3R83M) This video covers the theoretical and practical aspects of the Newton's Divided Difference as an interplation method. A numerical interpolation problem involves step by step construction of the divided difference table and interpolation procedure.

[Video 3. Newton's Divided Difference](https://www.youtube.com/watch?v=k9VH3dOYvA0) This video covers the Gregory-Newton (backward, forward, and central) Interpolation formulas, specifically generated for uniformly spaced discrete functions. Numerical example is presented after explaining the construction of difference tables.

[Video 4. Cubic Spline Interpolation](https://www.youtube.com/watch?v=IsOmJx9Or60) This video lays out the theoretical aspects of obtaining cubic splines coefficients for natural splines and linear extrapolation end conditions. A step by step explaination is provided using a numerical example.

[Video 5. Inverse Interpolation](https://www.youtube.com/watch?v=2UsJs4pjDm4) This video briefly covers the basics of inverse interpolation and goes over a a step-by-step numerical example.

[Video 6. Extrapolation](https://www.youtube.com/watch?v=6M2QdClq_i8) This video covers extrapolation using Gregory-Newton Forward and Backward interpolation polynomials. A numerical example is given that explains the procedure step by step.

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