Course

MATH-250: Advanced numerical analysis I

Lectures in this course (106)

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

Covers the numerical analysis of differential equations, focusing on methods and stability conditions.

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

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

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

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

Explores numerical integration, properties of integrals, composite formulas, and error estimation.

Explains quadrature formulas for digital integration and achieving accurate results.

Explores the composite quadrature formula, digital integration, and numerical integration techniques using interpolating polynomials.

Covers digital integration methods, including composite formulas and convergence order.

Explains capillary networks, blood exchange, hydraulic resistance, and pressure distribution in branches.

Explains methods for solving linear systems using matrices and algorithms.

Explains Gaussian elimination and LU factorization for solving linear systems of equations.

Explores the conditions for LU factorization without permutation and diagonal dominance in matrices.

Explains the Gaussian elimination algorithm with pivoting and LU factorization for linear systems.

Covers the Choleski factorisation method for solving linear systems efficiently.

Discusses precision problems in linear systems and the limitations of direct methods.

Covers iterative methods for solving linear systems, emphasizing convergence analysis and well-chosen matrices.

Explores iterative error calculation and the spectral radius significance in error analysis.

Covers the construction of an iterative method for linear systems by decomposing a matrix A into P, T, and P_A.