Lectures related to Lagrange Interpolation: Case 2

Interpolation de Lagrange

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

Differentiable Functions and Lagrange Multipliers

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.

Approximation of Data

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

Numerical Integration: Lagrange Interpolation, Simpson Rules

Explains Lagrange interpolation for numerical integration and introduces Simpson's rules.

Lagrange Interpolation: Numerical Integration Techniques

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

Finite Dimensional Spaces

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

Numerical Integration: Lagrange Interpolation Methods

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

Interpolation de Lagrange: General Case

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

Attack on RSA using LLL

Covers Coppersmith's method for attacking RSA encryption by efficiently finding small roots of polynomials modulo N.

Gauss-Legendre Quadrature Formulas

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

Linear Transformations: Polynomials and Bases

Covers linear transformations between polynomial spaces and explores examples of linear independence and bases.

Reed Solomon Codes: Basics and Applications

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

Sinc Interpolation

Covers Lagrange interpolation, local schemes, and sinc interpolation convergence.

Error Analysis and Interpolation

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

Numerical Analysis: Introduction to Interpolation Techniques

Covers the basics of numerical analysis, focusing on interpolation methods and their applications in engineering.

Lagrange Interpolation

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

Interpolation: Convergence I

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

Vector Spaces and Linear Applications

Covers vector spaces, subspaces, kernel, image, linear independence, and bases in linear algebra.

Interpolation of Lagrange: Dualité and Coupling

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

Numerical integration: continued

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