Finite Dimensional Spaces

Related lectures (30)

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

Covers polynomial identity testing using oracles and random point evaluation, with applications in graph theory and algorithmic aspects.

Explores trigonometric polynomials, emphasizing Fourier inversion and Plancherel formulas.

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

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

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

Explores integration on H_pxH and arithmetic properties, including norms, structures, and polynomial factorization.

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

Explores orthogonal and orthonormal bases, Gram-Schmidt process, and orthogonal polynomials in physics.

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