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Concept

Approximation theory

Related lectures (32)

Numerical Analysis: Jupyter Notebook Tutorial Log in to Mediaspace to watch this video

Covers course organization, Jupyter Notebook for Python experimentation, algorithms, interpolation, solving equations, linear systems, and practical applications.

Lagrange Interpolation: Numerical Integration Techniques Log in to Mediaspace to watch this video

Covers Lagrange interpolation and its application in numerical integration techniques, focusing on both non-composite and composite methods of quadrature.

Orthogonal Polynomials Log in to Mediaspace to watch this video

Explores L^2 bases and orthogonal polynomials, discussing their properties and applications in polynomial approximation.

Gauss-Legendre Quadrature Formulas Log in to Mediaspace to watch this video

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

Spline Interpolation: Definition and Error Analysis Log in to Mediaspace to watch this video

Explains spline interpolation and error analysis in approximating data points using piecewise linear and spline methods.

Interpolation Theory: Embedding and Completeness Log in to Mediaspace to watch this video

Covers the embedding of spaces and the completeness of spaces, exploring the connection between interpolation theory and approximation theory.

Taylor Polynomials: Approximation and Generalization Log in to Mediaspace to watch this video

Introduces Taylor polynomials for function approximation, starting with linear and quadratic forms and then generalizing to higher orders.

Numerical Integration: Lagrange Interpolation Methods Log in to Mediaspace to watch this video

Covers numerical integration techniques, focusing on Lagrange interpolation and various quadrature methods for approximating integrals.

Taylor Approximation: Matrix and Polynomials Log in to Mediaspace to watch this video

Explores Taylor approximation of functions using polynomials and matrices for quadratic approximation.

Numerical Analysis: Interpolation and Approximation Log in to Mediaspace to watch this video

Covers linear systems, non-linear equations, and interpolation for numerical analysis.

Polynomial Approximation: Stability and Error Analysis Log in to Mediaspace to watch this video

Explores challenges in polynomial approximation, stability issues, and error analysis in numerical differentiation.

Finite Elements Method: Error Estimation Log in to Mediaspace to watch this video

Explores a priori error estimation in the finite elements method, covering convergence analysis, orthogonality, weak formulations, and optimal precision.