Theorem 1.1: Interpolation and Equidistant Points

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

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

Explores constructing a piecewise continuous function using degree 2 interpolation by intervals.

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

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

Covers Lagrange interpolation using intervals to find accurate polynomial approximations.

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

Explores trigonometric interpolation for approximating periodic functions and signals using equally spaced nodes.

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

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