Lectures related to Piecewise Polynomial Interpolation: Splines

Introduces Lagrange interpolation for approximating data points with polynomials, discussing challenges and techniques for accurate interpolation.

Explores splines, emphasizing the least-squares method for interpolating splines and demonstrating its application using MATLAB.

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

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

Explores Lagrange interpolation, emphasizing uniqueness and simplicity in reconstructing functions from limited values.

Covers the concept of piecewise linear interpolation and the importance of dividing intervals correctly.

Covers the interpolation of nonlinear functions using Lagrange polynomials and error analysis.

Covers numerical integration methods, focusing on trapezoidal rules, degree of exactness, and error analysis.

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

Covers the basics of Newton interpolation and interpolation polynomials using Lagrange and Newton methods.

Covers the Lagrange polynomial interpolation method and error analysis in function approximation.

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

Explores interpolation of regular functions, error analysis, convergence, and Chebyshev polynomials.

Explores finite dimensional spaces, covering extraction process, bases generation, and space completion.

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

Covers Lagrange interpolation as a unique polynomial of degree 2N through 2N + 1 points.

Covers polynomial interpolation, error analysis, stability, and piecewise linear interpolation using equally distributed nodes.

Provides an overview of polynomial interpolation techniques in numerical analysis, focusing on Lagrange interpolation and error estimation methods.

Covers piecewise linear and spline interpolation methods, stability, convergence, and data interpolation using splines.

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