Uniqueness of Interpolation Polynomials

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Introduces Reed Solomon Codes, their applications, polynomial definitions, interpolation, roots, and the Fundamental Theorem of Algebra.

Covers the least squares method for approximating data and handling errors.

Explores Gauss-Legendre quadrature formulas using Legendre polynomials for accurate function approximation.

Introduces the problem of interpolation and demonstrates challenges with adding more points.

Covers the convergence theorems for interpolation and the application of polynomials for equispaced points.

Explores error analysis and limitations in interpolation on evenly distributed nodes.

Covers the topic of approximating functions using polynomials through interpolation, emphasizing the importance of optimal point selection.

Covers Lagrange interpolation, focusing on constructing polynomials that pass through given points.

Explains the Lagrange interpolation method for arbitrary n and constructing polynomials through given points.

Covers the optimization of error in polynomial interpolation, focusing on minimizing the error by strategically placing interpolation points.