MATH-250: Advanced numerical analysis I

Lectures in this course (106)

Covers the principles and applications of linear regression, focusing on building a simple model to make suggestions.

Covers the convergence theorem of Newton's method for nonlinear equations.

Explores the stability of progressive and retrograde Euler methods in numerical simulations.

Discusses stopping criteria for fixed point iteration in nonlinear equations and how to manage errors.

Introduces QR factorization for matrix decomposition, emphasizing its importance in various applications and the implications of a well-chosen model.

Discusses stopping criteria for fixed point iteration and Newton's method in nonlinear equations.

Covers the solution of a 2x2 system of differential equations using matrix notation and explores stability methods and specific cases.

Covers the Fourier transform, compression techniques, and spectral analysis of periodic signals.

Explores data compression fundamentals, techniques, and information preservation.

Explores interpolation applications in biological tissue and population census data analysis using the method of least squares.

Covers diagonalizing matrix A into VDV-1, stability of Euler method, and solving systems with progressive and retrograde Euler diagrams.

Covers the concept of Fourier series and their practical applications in signal processing.

Explores the uniqueness of interpolation polynomials and the role of distinct data points in the interpolation process.

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

Explores the Discrete Fourier Transform, Fast Fourier Transform, orthogonal functions, and trigonometric approximations.

Explains how to find the polynomial of interpolation using the Vandermonde matrix.

Discusses corrections to old videos on convergence methods and precision.

Covers the iterative method for approximating Greek functions and stability conditions.

Explains Lagrange interpolation, constructing polynomials passing through given points with explicit formulas and calculations.

Discusses periodic functions, integrals, and approximations using trigonometric polynomials and proofs of related theorems.

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