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Lecture
Curve Fitting: Polynomial Interpolation
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Approximation of Data
Covers the least squares method for approximating data and handling errors.
Polynomial Interpolation: Lagrange Interpolation
Covers Lagrange interpolation as a unique polynomial of degree 2N through 2N + 1 points.
Interpolation by Intervals: Lagrange Interpolation
Covers Lagrange interpolation using intervals to find accurate polynomial approximations.
Piecewise Linear Interpolation
Covers the concept of piecewise linear interpolation and the importance of dividing intervals correctly.
Numerical Integration: Basics
Covers digital integration, interpolation polynomials, and integration formulas with error analysis.
Interpolation of Lagrange: Dualité and Coupling
Explores Lagrange interpolation, emphasizing uniqueness and simplicity in reconstructing functions from limited values.
Polynomial Interpolation: Error Analysis, Stability
Covers polynomial interpolation, error analysis, stability, and piecewise linear interpolation using equally distributed nodes.
Polynomial Interpolation: Curve Fitting
Explores polynomial interpolation for curve fitting, error analysis, and the Runge's phenomenon.
Interpolation de Lagrange
Covers Lagrange interpolation, focusing on constructing polynomials that pass through given points.
Nonlinear Equations: Interpolation and Error Analysis
Covers the interpolation of nonlinear functions using Lagrange polynomials and error analysis.